I had no end of Bluetooth issues with my new iMac, running Mojave upgraded from High Sierra ( not a clean install).
I went though all the usual things to resolve it. Somewhere along the way it seemed to be “fixed”, I don’t know why.Worked perfectly for about 2 months,.. then the problem came back worse than ever. Same thing, ..tried all the fixes as before but things just got worse.
I bought a Mac specific wired keyboard and mouse as I had given up on Bluetooth.
Then in one last attempt to resolve this ( never give up attitude ) , I saw a mention of Android file transfer as a possible cause. The same post included eye to helper as another.
Turns out Mojave dosen’t Play well with these,..they worked perfectly for me in High Sierra.
They will try to open at login, which they can’t, being incompatible with Mojave. But system keeps trying, resulting in strange behaviour and issues.
There are hidden files associated with these apps that need to be removed to completely delete them from system.
Search on how to do this, follow the guides and while your at it delete the Bluetooth p.lists before rebooting after removing offending files.
My Mac is now running faster, no issues with Bluetooth nor anything else.
Android File Transfer was most likely the culprit, eyetv helper could of been also, ..but not sure of which.
Since I use neither on this Mac, the removal was no issue.
Problem solved for me.