My recently acquired 86 4runner

I can't really tell if going from H2 to H4 does anything. The 4x4 control lever doesn't really feel like anything is engaging between H2 and H4. The lever itself can easily slip between one and the other and there doesn't seem to be any real change.

L4 does seem to engage and the light on the dash lights on. Although it doesn't seem to engage every time.

Should the H2 - H4 feel like that?

I live in the city and haven't been able to really test it off pavement .

 

on pavement at low speeds (like in a parking lot) when you are in 4x4 low or high and you try to make a turn you will feel the vehicle "buck jump" as the drivetrain loads up and releases. one tire will slip/skid momentarily then grab again, it will also take some throttle to move when cornering whereas in 2wd it will coast around a corner.
Another test for this is to jack up the front end and turn the front driveshaft with your hand, in 2wd you should be able to rotate the shaft which should also rotate your front axles and if your hubs are locked your front tires. In 4wd it should be locked to the rear driveshaft through the transfer case and will not spin by hand.