These Units use White-Rodgers Solenoids, Power goes thru both in forward and reverse. Normal close side on one and activated side of the other. you can not see burnt contacts inside. If it work in in one direction and not the other and you can hear or feel the solenoid close or activate, the one of them is most likely bad. directional problems tell me motor is good. bad contacts inside of the solenoid. Very Common problem.

my wag is on the switch in the control handle,

Why do people not update others who are trying to help LOL. By the way my money is on broken wires in the tiller harness where is passes over the drive motor LOL

get a multimeter and check your circuits
you cant correctly diagnose a solenoid or a switch by touch or feel or listening to it

That should be 3 speeds. The 2 big solenoids are F and R, and the little ones are 2nd and 3rd speed, and lift pump. Just because you can hear and feel the solenoid activating doesn't mean it's working, if you are talking about the large F solenoid. If it doesn't click, then I would check to see if it's getting power when you twist the handle. If not, then check the switch in the control handle. If you listen carefully, with the key off, you can hear the little switches click. Should be 3 clicks going forward and 3 in reverse.