Well,
EM fluctuations in off the grid facilities that are coincident with temperature drops - using DC equipment with separate and isolated power (lol....I love that one....they were batteries). Audio anomalies. Eyewitness accounts/testimonials (some even from skeptics) of localized foul smells, otherwise unexplained object movements, strange sounds, strange sights, etc.... Video anomalies. I suspect you know the drill.
So that is evidence in support of. Some of it anecdotal. some of it measurement. Is it Proof? Not at all (not even close). Is it even good evidence? Debatable - some of it is certainly interesting. Interesting enough that if I were retired and didn't give a crap about my reputation, I would investigate it further - and a bit more properly. But its evidence none-the-less.
The fact that much of the evidence might be explained by something other than ghosts (or whatever the pseudo technical term is) - malfunctions, hysteria, mis-interpreted natural phenomena - is relevant and important - but unless those alternative explanations can be proven reproducibly (and few seem interested in doing so), they are only plausible. Thus the claim of evidence (not proof) of ghost phenomenon holds. I am not opposed to a bit of Ockham's Razor here, but even that needs some confirmation in some cases.
Not really sure why that bothers some people - you know, that evidence can exist for something that may not be true (or might).
Think about a courtroom. Evidence is presented from both sides - each supporting a different premise. Only one premise is true, but there can be evidence for both. Of course, in the courtroom they also get to suppress that which doesn't support their claim. Good science doesn't intentionally do that.