The MacGyver skill.
It allows a character the ability to implement strange fixes to common items or use common items to fix strange things.
Consider it the skill to determine one's ability to convert the strange to the common and vice versus.
Need an small explosive charge? Typically, you'd need some base explosive, electronics, and a detonator. With Toaster Repair, you'd only need a bucket of lard, an orange (more mold the better), a roll of pennies, and a knitting needle.
Need to jump start a car, but don't have anything typical to jump it with? Use Toaster Repair to figure how convert some strange alien artifact to an effective car battery.
Need to repair a unique pre-war weapon? Normally, you'd need very specific knowledge to accomplish this goal and quest for the parts and pieces... but with Toaster Repair, you only need two packs of chewing gum, 6 baseball cards, the scratch off material from a lotto ticket, and a turkey baster. Sure, it might fall apart again, but then a new fix will be thought of.
Need a cure for a nasty case of the crotch rot? Sure, you can get antibiotics and rest for a week... OR... With Toaster Repair, you'd be able to get that Ranger back in action with a quart of moonshine, some glowing material from that lead lined container you found, a toilet brush, and one chicken egg. The ranger may turn green, have delusions that gnomes are stealing his underwear, and grow a fondness for flower arrangement... But no crotch rot!
I think Toaster Repair should allow strange solutions and creations in even stranger ways. I'd suggest the developers take a look at Mad Scientists from Deadlands or Junkers from Deadlands: Hell On Earth. (Classic editions, please.) Read the craft mechanics for both and pay attention to some of the crazy failures that can happen.
EDIT: Mechanics wise... I think it'd be a skill that is used to attempt to override repair, rigging, fixing, crafting, and etc. mechanics at the cost of a much, much lower chance of success, but the ability to make use of any assorted junk you've been carrying around. The more stuff you use and the more bizarre the collection, the bigger the bonuses you get for the check. If the check fails, you lose a certain amount of the fodder you put forth depending on how bad the failure was. If the check succeeds, all the fodder is used, but you bypass the problem. There should be as equally ridiculous successes as there are failures with a HUGE variance in possibilities. Keeps it risky and entertaining.