I think @KoolDude already sent a lot of info about compressed ECA symptoms, but here is a “tabloid” type of article with symptoms caused by temporal artery insufficiency.
Temporal artery is branching off the ECA, so if the styloid process(es) affect(s) the ECA(s) (external carotid artery), it can reduce blood supply to the temporal artery(IES) mimicking the temporal arteritis.
Here is a bit more reputable article about the same condition
