What does the whole button design look like… Have a photo?
Here should be your whole shifter type,
Condition: Used.
www.ebay.com
Seems Mercruiser now has a couple designs looking things over for the button.
Like item 16 for example kind of looks a cap/cover,
https://www.mercruiserparts.com/bam/subassembly/32079/8457/34
Or more probable item number 7 with a stem,
https://www.mercruiserparts.com/bam/subassembly/32079/8457/51
Your model design name should be Mercruiser shifter control 4000 Gen 2 that if ever needed new cables Gen 2 cables are what you’d be looking for.
Remote Controls and Components - 1994 & Up
www.mercruiserparts.com