There is quite a bit of look-loo experience to support that queens do not shut down completely. They do slow substantially and take pause a day here a day there. However, there is always some brood/eggs on the go 24/7/365. It may be very little, as little as 50-100 cells mid dead winter, but there nonetheless. When looking for evidence of queen in fall/winter; first figure out where the centre of the tight cluster is. Look there. The queen will not be roaming about the hive. She will be huddled centre/centre. Do not expect to easily see the few cells or the queen under the mass of bees. In a healthy well organized hive ramped down for fall and drifting into winter, both will be there. (queen and a small brood patch)
Complete absence of brood/eggs means either there is no queen, or there is a queen which is virgin or defective.
Perhaps just as a comparison or reference at this point in time (Sep25). Here in the north, my queens have slowed down. When I look in the hives this week I see 2 frames with palm sized patches if eggs/larvae both sides. I also see between 3 and 4 peppered frames left of matured emerging brood. A week ago those ones where -sheets- of brood covering 70% of the frames both sides. Now as a bee comes out, every cell is being backfilled with the syrup being fed. Point being, your hive(s) should still be raising new palm sized patches of brood on 2 to 3 frames at this time. The main mass winter bee brood cycle should emerging/emerged and the bees promptly backfilling the nest as those cells come open.
.... completely broodless means queenless or a dud queen regardless of season, imho. I do not believe your issue is the season.
Hope that helps! ... in some way.