Pictures help a lot! Now that you (and we) know that its not a relay but a thermal overload protector, I would go with your 15 amp fuse test. If it burns - you have a problem downstream. If it works and powers the downstream items as normal then you probably have a bad thermal overload and need to find a replacement.
Her's some from Amazon with a push button reset:
https://www.amazon.com/Aramox-Overlo...omotive&sr=1-8