In the old days the door open was detected by a plunger/button on the door shut. Have a look to see if there is anything that looks like a pimple (the switch would be under a rubbery/plastic cover to keep it clean/dry).
If not, then the detection may be via a micro-switch on the door latch mechanism. You'll have to remove the door card and see whether the plug (it'll be tiny) is still attached, clean/not corroded etc. and give the switch a spray with something WD40-ish to unstick anything sticky.. but grease it up again if the cleaning flushes out all the existing grease.
If the switch/contacts has packed up, from my experience with a boot latch, they aren't available as a separate item and the easiest thing is to just stick a new one on there. It doesn't affect the door locks or the c/locking etc.
Ralf S.