First, please turn off your caps lock. All-caps is considered shouting.
Second, chances are the amount of light from a glow-in-the-dark face on a timer wouldn't cause problems for paper unless you get the paper very close to the timer. For added safety, try to position the equipment such that the timer's face doesn't point directly at any point where your paper will be. For instance, you might raise the timer a foot or two above the level of the enlarger, and position the timer so that paper never directly crosses its path, to minimize exposure when you're putting the paper on the easel.
FWIW, I've got a Philips PCS130 enlarger with a PCS150 light source. The PCS150's control box has four lighted dials. This isn't just glow-in-the-dark stuff; the dials actually have low-wattage bulbs under them. When I first got the thing, I was concerned that they'd cause problems, but I've noticed no fogging because of these dials. My PCS150 is placed about a foot to the right and above the enlarger's baseboard, and my paper safe is to the left of the enlarger, so the dials don't shine directly on the paper at any point. This seems to be sufficient protection. Although I've not done safelight tests on the dials themselves, I have done safelight tests for my overall level of darkroom lighting, with the PCS150 turned on, and I've found no problems. If the lighted dials of my PCS150 don't cause fog, I doubt if a glow-in-the-dark dial would.