The official Jordan Pass offers waiving of Jordan visa fee, but only if you stay in Jordan for three consecutive nights:
part of the pass's benefits is that it waives the visa fees (40 JDs) only if you are staying 3 consecutive nights and buy it before arrival to Jordan.
How do they define "night" is unclear. For example, assuming my arrival is July 1st, and I am departing on July 4th at 2am - so as long as I pass immigration after midnight on 4th, technically I am in Jordan on three nights if they look at dates. But if they consider "night" as "hotel stay in Jordan", then I am not.
How does "three consecutive nights" are calculated, as calendar dates or actual hotel stays?
Update: I also emailed the Jordan Pass website through their contact form asking this exact question. Here is their reply:
Yes but please make sure not to stamp your passport before 12:01 am of July 4th, otherwise, they will ask you to pay for your visa.
This is what I expected, but not exactly matching the "full 3 nights" described on their website, so I wonder how does the Immigration applies it. Thus I will leave the question open until someone comes up with personal experience on that matter. Or until I do this myself.