2002 f150 4r70w, sometimes wont go in reverse, i also have a long 1st to 2nd shift, i am pretty sure that is the accumulator, but the reverse issue is confusing me, when cold goes in most of the time, but after a drive it wont go in, if i get out and rock the truck back and forth it goes in every time i do that, when i rock it, i think i hear a click in the transmission, any help would be appreciated......

 

Reverse from the shifter through the linkage is purely a mechanical actuation at the transmission. There is no solenoid involved for a one gear reverse operation.
The internal fluid flow and pressures are in effect for all functions..
Check/lube/adjust as needed to be sure it's not an outside issue.
Time to have the trans fixed either way for all the issues.
Good luck.

 

This is dangerous , I hope you've already done something about it