That's not true Service T. This truck is 12v until 3rd speed. Then it's 24v to the drive motor like the OP said. Tricky lil trucks sometimes. Interesting way of doing it.

Remember that it's set up that two 12v batteries (two 6v batteries in series = a 12v battery) are in parralel. In high speed 24v goes to the drive motor but the rest of the machine is stil only 12v.

I'm looking at a schematic. Here's what should happen:

-1st speed (F or R) - only the F or R switch closes which pulls in the appropriate contactor. Motor current is forced through a resistor causing the motor to spin slowly.
-2nd speed (A contactor) - F or R switch is closed along with the A switch which then pulls in the A contactor. This bypasses the 1st speed resistor allowing thw full 12v to the motor.
-3rd speed (B and C contactor) the B switch is actuated in the handle pulling in the B contactor. The C switch is located on and actuated by the B contactor.
There should be a little actuating arm on the moveable tips of the B contactor that presses in the C switch actuating the C contractor. Sometimes you need to adjust it (bend it in a bit) so it actuates the C switch properly. IIRC, its just a little hook looking metal piece screwed onto the movable tips of the B contactor.
At this point the B contactor removes the negative side of the parralel circuit from one of the 12v battery sets and sets up half of the series circuit. The C contactor provides the second half of the series 24v drive circuit and isolates the drive motor circuit from the rest of the machine which is now still using 12v but from only one battery set.

Whew.

Here's a quick test. When the B contactor pulls in, can you raise the mast? That little switch on the B contactor has two circuits in it. One to actuate the C contactor and the other disrupts the lift switch circuit as mentioned before. If you can raise the mast with the throttle at full speed, something is wrong with that switch or its wiring.

Tracing wires and cables in these can be a pain since everything gets bundled up and ran behind the contactor panel.

I had a customer who had 5 of these. Got to know them pretty well. One of the major dealers was literally across the street. Right before I took over the account they shopped one for this same issue, couldn't fix it and charged something like 2500 for the failed attempt. Needless to say the customer dropped said dealership for service lol.

If you want a copy of the schematic, email me. My email is in my profile. It's 2 pdf pages. Simple on paper compared to the spaghetti you're looking at. Lol