Very strange.

I have P245/75r16 tires on a 98 Sport.  Makes speedometer off by 13pct.   I ordered a manual reduction box and got the speedometer back to normal readings.

But now I occasionally kick off a P1875 code after installing the reduction box.  Never tripped the code before I installed it.   

Coincidence? 

 Time to crawl under and check wires and connections first but very strange.

I'm looking at an SQ series FSM, as I don't have one that specifically relates to your SV series vehicle, and what triggers the P1875 code, at least on an SQ series vehicle, is defined as "Vehicle speed sensed by vehicle speed sensor is more than 10 km/h higher than that sensed by A/T output speed sensor".

Now - if I understand what is happening - you've inserted a "speedometer correction gearbox" in between the speedometer drive gear in the transfer case and the speedometer cable to correct the speedometer "under-indicating" as a result of the increased tire size, which will cause the speedometer to indicate a higher speed than it normally would.

If I'm not mistaken, the VSS (Vehicle Speed Sensor) on a Sport is located in the speedometer itself, so the correction gearbox will force the VSS to register a higher speed, and the ECU is seeing this as not matching what is reported by the transmission's output speed sensor, which should only happen if the vehicle is in low range, but the low range switch is not reporting the vehicle in low range (because it's not), so the ECU sees this mismatch as a fault.

What's the fix ...

Most speedometers "over indicate", in theory, so that the vehicle operator cannot blame the vehicle manufacturer if he gets a speeding ticket - try setting the manual reduction box (if it's adjustable) for a 8 or 9% correction factor, which should get the display close whilst at the same time keeping the discrepancy between the two sensors low enough that it does not trigger the code until/unless you're travelling at a high rate of speed.

P1875 (37) 4WD Low Switch Circuit Malfunction. You can have the list at http://www.troublecodes.net/suzuki/

I'm looking at an SQ series FSM, as I don't have one that specifically relates to your SV series vehicle, and what triggers the P1875 code, at least on an SQ series vehicle, is defined as "Vehicle speed sensed by vehicle speed sensor is more than 10 km/h higher than that sensed by A/T output speed sensor".

Now - if I understand what is happening - you've inserted a "speedometer correction gearbox" in between the speedometer drive gear in the transfer case and the speedometer cable to correct the speedometer "under-indicating" as a result of the increased tire size, which will cause the speedometer to indicate a higher speed than it normally would.

If I'm not mistaken, the VSS (Vehicle Speed Sensor) on a Sport is located in the speedometer itself, so the correction gearbox will force the VSS to register a higher speed, and the ECU is seeing this as not matching what is reported by the transmission's output speed sensor, which should only happen if the vehicle is in low range, but the low range switch is not reporting the vehicle in low range (because it's not), so the ECU sees this mismatch as a fault.

What's the fix ...

Most speedometers "over indicate", in theory, so that the vehicle operator cannot blame the vehicle manufacturer if he gets a speeding ticket - try setting the manual reduction box (if it's adjustable) for a 8 or 9% correction factor, which should get the display close whilst at the same time keeping the discrepancy between the two sensors low enough that it does not trigger the code until/unless you're travelling at a high rate of speed.

"Vehicle speed sensed by vehicle speed sensor is more than 10 km/h higher than that sensed by A/T output speed sensor".

OK, makes sense..     

But from what I am observing,  It seems to only throw the code after the vehicle sits overnight.    And trips within 1 mile of leaving the house in the mornings  Mornings are 50-65 Degrees F. 

I drive 36 miles one way to work,    I clear the code when I get to the office and drive it at lunch and on the way home and no 'money light', another 35-50 miles for the day. 

This has happened two mornings in a row.   I want to see if it is a pattern or gathering any more details.  If it is then its even more weird because I would expect it to set again right
after I clear it when I drive away again.
 
The speedo adapter box isn't adjustable.     

If the speedo corrector is what I think it is, removing it should take no more than a few minutes - try removing it and see if the error goes away, if it does, reinstall and see if it returns - that way you'll know if it's related.

I also have a Sport with an automatic transmission. I have struggled with the P1875 code for a couple of years. My original check engine light came on during a ZukiWorld trip. I didn't have anything to read the code during the long off road trip. I was also having torque issues, which we were not sure was related or not. My rig has issues above 5k feet.

I can clear the codes and it will come back after x number of miles or after driving and a restart. Like Banjoman stated, it comes back on the next morning (restart).

I have replaced the automatic transmission speed sensor, with a used one. I was not able to find a new one. I also replaced the short section of wiring harness between the transmission speed sensor and the main harness, because the connector was questionable.

The speedo was replaced with a used one, but maybe it had the same failed VSS issue.

The low gear switch on the transfer case was replaced, but it didn't make a difference.

Some of the codes will only appear after they happen "x amount of times" in a row.  Check after driving home and see if there is a 'pending' code.

Some of the codes will only appear after they happen "x amount of times" in a row.  Check after driving home and see if there is a 'pending' code.

I'm reading this code is one of them.   I need to sit down with the FSM and the 98 wiring diagram which I both have.

.

I'm reading this code is one of them.   I need to sit down with the FSM and the 98 wiring diagram which I both have.

.

I put in a scanner that can show pre codes and am still getting the P1875 codes.

Removed the speedo adapter and took a ride.  The same P1875 codes are still registering and eventually tripping the Service engine light.

I even left the vehicle idling for a while and even then the code are registering so  I put the speedo adapter back as  I don't think the hardware is speedo adapter
is playing a role. 

More reading and reviewing ahead.

Those specific codes are the hardest to track down.

Those specific codes are the hardest to track down.

Been out of town for a while. Finally got a a chance to do some checking

Pulled the connector on the 4Lo switch to check continuity - Set meter to 'audible tone' 

4H 2H   -  infiniity

4lo  - should have gotten 'continuity with audible tone' but meter values changed from 1 to around 5.00 but no audible tone.

Manual states

1 disconnect negative batter cable - did this
2. Disconnect 4WD low switch coupler
3. Check Continuity between 4wd low switch terminals   -   continuity 4lo    infinity 4hI AND 2HI 

As I could not get an audible tone from the Meter I 'think' the' switch may be bad. 

Can you take the switch apart and clean it?  Contacts might just need a bit of sanding.

Can you take the switch apart and clean it?  Contacts might just need a bit of sanding.

ordered a new switch,    It's coming from 'who-knows-where-it-stan..'  so it'll be here beginning of Dec.. Until then I'll deal with the light and clear it as needed.

Doubt it but I do have a rebuilt ECM for this vehicle I may swap out just for 'SHI*S and GIGGLES' to see if it makes any difference as that is part of the diagnostic.

ordered a new switch,    It's coming from 'who-knows-where-it-stan..'  so it'll be here beginning of Dec.. Until then I'll deal with the light and clear it as needed.

Doubt it but I do have a rebuilt ECM for this vehicle I may swap out just for 'SHI*S and GIGGLES' to see if it makes any difference as that is part of the diagnostic.

Followed FSM checks to the letter,   New 4Lo switch,  even a new computer,   no wire breaks in the circuit.  Still got the code popping up.

Larger tires and / or the 4:23 transfer case gears are probably doing this.

Now that you've fixed the switch, take the speedometer correction gearbox out and see if that fixes it.