Obviously the preferred solution is to get an exact replacement for that fusible link. With the make and model, which you have, an internet search may turn up parts lists and suppliers.
Supposing that the part search, after much effort, is futile. If it was mine, I would as a last resort bypass the link and run it as desired until it fails. Not much danger to you or your premises in doing so.

Is there some sort of sentimental value attached to the shop vac? If not, buy a new one on sale, with a warranty. They are not that expensive. Or buy one used on craigslist for next to nothing.

OK, so it looks like it may be a fusible link with the cover over the protruding ends removed and the link between them melted.

From what I read, you measured the resistance between the two exposed terminals and had continuity when a piece of wire was placed across them - so you read the continuity of the wire jumper.

This is a FUSE - an overload protection device! You DO NOT just jumper it over as suggested. You need to find what caused the excessive current draw, and the fuse to open, in the first place.

With products such as this, buildup of debris and dirt, arcing of motor brushes, motor bearing failure, or shorts in the motor windings could all cause excessive current draw.

Clean everything up, lubricate brass bushing/bearings, clean and use electrical contact spray cleaner/oil on the armature, and then jumper a fuse, based on the product's current draw label, using clip leads across the fusible link.

If it blows, you've probably got problems that exceed economical repair - if not, order the replacement link, and you may be good to go for years.