Re: 1975 Johnson 135 any good?
That sounds like it might have the high compression heads on it. If so it oughta be a strong running motor.
Like limit said, there should be a relay box to control the trim. If it's been upgraded it will be under the cowl, mounted to the back of the motor. If not there'll be a box somewhere in the boat near the transom. The cover measures 'bout 4 1/2 x 6".
re. Trim: If it's a 'plumbing' problem they're purty easy to rebuild, just some seals & a few o-rings. If the pump motor's bad a replacement runs a couple hundred bucks or so. But before you order one make sure you've eliminated all other possible causes. ie. Bad wires, connections, relays, switch, etc.
The trim motor should have green & light blue leads coming from it. Easiest way to check it is deliver 12V directly. If'n ya touch the leads to the battery the trim should move in one direction. Reverse the leads & it should move in the opposite.