Hotel sitting requests likely happen more in destination vacation places, but considering this owner wants their pet cared for while away at a funeral, I would be less guarded. I would still arrange for a meet and greet with the dog at the hotel (start by meeting in lobby or other public space) before accepting the booking. Like other housesitting bookings, you have to follow your instinct based on the conversation and meeting. Most of the time, It seems that people are genuinely looking for care of their pet. Still I advocate to leave a paper trail & an electronic trail of your whereabouts (with arrival/departure times, the location) and check in with a friend. I’d also confirm that a no housekeeping service can be hung on the door And the front desk has that marked in their system accordingly, so that no service employee tries to open the door while you’re there.
Personally, I wouldn’t feel the need to bring anyone along nor would I require a crate. Instead of a previous suggestion to have an hour transition when no one’s there with the dog before you arrive, I’d suggest you ask them to have their pup dressed (leash, harness, collar with ID tags) for a walk at a specific time (which you must arrive for on time). You could meet them outside their door or in the lobby. You would not have to actually walk the dog at that time, but you could walk it back on up to the room. If they’re hiring someone to stay with their dog during the funeral, it’s probably because if no one‘s there the dog will have separation anxiety and bark excessively or scratch at the door to try to get out. If a dog who is experiencing separation anxiety is left alone in the room after owners leave & before you arrive, then when you finally open door, chances are very high that it would bolt. It sounds like these are responsible owners who are trying to avoid problems with the hotel during what might already be a stressful time.