It's not rocket science
You don't have to take wild guesses
First establish it the remote
Take the batteries out, the fact it's flashing while driving (sending), probably means you can skip this step, I wouldn't, for the sake of 10 seconds and a test drive, I have seen weird unexpected results when double checking things and end up going down a different path
Then establish if it's a problem with the buttons in the shell or on the PCB
Try PCB without the outer shell
It's 50/50 whether it's a button pushed in too far on the shell or a faulty button on the PCB
Either reshell or change the button
Just for clarity
We are talking about one of these
Physical button not membranes
It's not the ECU or body computer or anything in the car in my opinion
The button are replaceable
They are surface mount, but they aren't that difficult to change with the correct equipment and skill, they are quite big pads by mobile phone standards
If you are near me (Crewe) and If needed, if you supply the buttons around a fiver for three, I will change them free of charge
It's quite easy to change the shell, just make sure you order the correct one
The inside from one type will not fit the other
Odds are it's the second
Be careful taking the PCB out, it's easy to damage the component on the thin strip, top right on the picture of the PCB