New owner with few questions, Brake light always on! Options

[PaIsa]

Hello! New 914 owner here with a few questions.
First the car: 1.7 (I think) 1972 914 with carburetor, Irish Green resprayed.
The issues:
1. Brake lights are always on. As soon as we put the key switch to ON, the rear brake lights come on even without touching the brake pedal. Looked at all the bulbs and everything is fine. Looked at wiring; did a repair on the front left ground wire but the rest seems OK. Looked at the switch on the master cylinder; it is there, but not sure what to look for. Any idea as to where to look to try to solve this.
2. Vibration: We have a steering wheel vibration when cruising at around 90-100 km/h. Where should I look first: wheel balancing?
3. Speedo not working: Our speedo is not working but I think that our issue is at the back of the car. We have a small tranny oil leak that seems to come from the speedo gear set-up. I did not open it yet but I guess that a first test that I should do would be to take the cable off, put the car in gear and see if the system for the speedo actually works.
Would be all for now.
Thanks