Hello,
I bought my first Samurai, it is a 1986 JX tin top.  I am really looking forward to fixing it up, but I have run into a problem.  The battery is not getting a charge from the alternator, even though the alternator is working (I had it checked). 

The following is a detail of the troubleshooting:
1.  Battery voltage does not increase when I start the engine or rev it up
2.  I tested the positive post on the alternator and it is putting out 16v when the engine is running, but the voltage at the battery is around 12.5v and does not increase when the engine is running.
3. I checked all the fuses and they are good.
4.  The battery light on the dash does not light up at start up.  I checked the bulb and it is good.

Does anybody, know what I should check next?
Thanks.

Sounds like the battery is starting to go bad, the plates slowly
get grounded as the battery ages, and it could also ruin your
alternator from excessive load

Wild

2.  I tested the positive post on the alternator and it is putting out 16v when the engine is running, but the voltage at the battery is around 12.5v and does not increase when the engine is running.

There's no way you can have 16V on one end of a piece of wire and 12.5V on the other - unless the wire is broken in the middle - and if I'm not mistaken, that particular piece of wire is also a fusible link - my guess is the fuse opened.

Excellent call Fordem, I change my opinion, check the wire

1 added TP for you

Wild

Thanks for the tip!  It seems that there is a break in the wire between the positive terminal of the alternator and the battery for sure. 
I hooked up a temporary lead from the positive terminal of the alternator to the battery and the voltage at the battery now will increase at startup AND the battery light on the dash lights up then shuts off at startup.

Now I need to find out where the wire is broken from the alternator.  I checked the fusable link for continuity and it is good.   I looked at the fuse box and there is not a fuse for the alternator. Any ideas where to check next?

Thanks.

Looking at the parts catalog for an 86 Samurai, it shows a short length of wire, called "wire, generator", that runs between the alternator and the main harness - so I'd start at the alternator and follow the wire to see where it goes - maybe the joint between the two has corroded - other than that I'd think you're going to have to either strip the harness or take the easy way out and make a permanent bypass.

If I make a permanent bypass, should I put an inline fuse on it, and if so what rating?
Thanks.

Good question - the original harness makes that connection through the fusible link - so if you're bypassing that fusible link, then yes, you should fuse it, and you need a fuse not less than the alternator output - I'd go with 60A.