Tank is on electric, not gas.
No drain visible, but I think there must be one, so perhaps it's behind the tank.
I ran the shower and observed what I could.
No active leaking that I could see.
Definitely (pre-existing) water damage to walls and floor, and some black coloured mold -with no apparent scent- on one wall.
The smell was relatively faint this time.
I couldn't pinpoint where the smell was coming from, but it doesn't seem to be from the floor, the spigot, any of the other interesting points on the tank, or the walls.
Most concentrated at the tank itself, between it and the wall shared with the shower.
The smell is not sulfur or otherwise particularly foul. My best go at a description is that it's a bit "sweet" and along the lines of a lightly smelly shoe, or sweaty hockey gear (hate that smell), wet dog hair, or a rug that's been left out in the dirt and rain.