Ignition switch problem or Transmission problem?

**Intermittent, leaning more towards always doing this** MANUAL transmission

When i put the key in the ignition, turn it 2 clicks ( 1 away from turning over the enigine), SOMETIMES ( mostly when its in reverse, but not always ) , none of my dashlights come on, and when i try to crank it, it jusr runs the starter, as if there is no fuel supply. it doesnt mattter how many times i try it from there, it wont start.

I've found that if its in first gear and does the above symptom, i so far have always been able to get it started again by turning the key all the way back ( sometimes even removing / reinserting ) , and clicked it twice very fast over and over again until the dashlights come on, and at that point i know the car will turn over properly and start.

But sometimes, even after starting it in first gear, if i put it into reverse, it shuts itself off>???

My personal opinion is that some of the contacts on the inside of the ignition switch is either sticking open, or sticking closed, whatever one it isnt supposed to be doing.

I can buy one for 60$, but do i have to have BMW recode it or something????

Any help would be great thank you!