I recently nicked the threaded piece of the valve stem on one of my tires. Since i needed to fix this immediately, i took it to a nearby garage to get a new stem (without a transmitter) so i could at least drive around town. They told me i needed to buy a new transmitter (cost $150 ish). 2 questions:

1 - the warning light only rarely comes on. i understand that this should be on continuously since there is no transmitter installed (or more accurately 3 of 4 are installed). Does this indicate a problem.

2 - do i really need a new transmitter (i see them online for $55 ish). Or can i Just buy a valve (~$5). i also see this valve online but not clear if i can just swap it onto the transmitter I have?

many thanks.