JohnGalt,
Well the prolonged standing is probably a contributing factor, especially since your symptoms seem to increase at the time.
Flat feet could potentially play a role as well. You may want to try out some OTC arch supports. Sof sole and Superfeet make some decent inserts.
If you are standing on a hard concrete surface, make sure that your shoes have good cushioning.
I would suggest that you try to move around the area as best you can as opposed to standing in one place for long periods. If you can’t move around much, shift from side to side, squat down for a few reps, and try some stretches.
Sometimes, the decreased exercise can result in increased tightness/soreness. I know it always seems like I start getting more aches if I don’t get to workout for a week.
Also, the illness may contribute to the aching as well.
You would also want to try to determine if the pain is myofascial related to the glutes as you suspect or if it could be referred from your back, which is possible. I would suggest that you use a towel roll behind your lumbar curve when you sit, to help decrease the postural strain on your back due to sitting.
Take care,
Ryan