I’m an electrician but many times I find it difficult to help people with questions like these when they aren’t even knowledgable of the basics of electricity and electrical troubleshooting. Electrical work isn’t what I consider to be a weekend warrior or handyman type of discipline, and it takes a great deal of knowledge to be effecient at electrical troubleshooting. I’ll try to help you even though I’m not even sure what your electrical knowledge level is, or if you even know how to use a digital multimeter, let alone an analog meter.
A windshield wiper circuit basically consists of the wiper motor, the multifunction switch which determines the frequency and duration of the wiper cycle, and the pulse or frequency module (electronic circuit board) which basically is the device which really controls how fast your wipers will cycle back and forth. Also of course is the fuse. I’m not going into great detail here but when troubleshooting always start from easiest problem to fix first. In this case the easiest problem to fix would be your fuse, so check that with the Ohm/resistence function of a meter for an open fuse (assuming you know how to use a multimeter).
I’m not sure where to start with this one, since you’ve mentioned that you’ve attempted some of the repairs yourself. Like I’ve said above electrical work and troubleshooting isn’t a handyman or do-it-yourself type of discipline so if you don’t know what you’re doing then you shouldn’t attempt it. I find it extremely odd that none of those mechanics could help you. Feel free to ask me any further questions though.