Electrical – Ceiling fan lights brighten when fan turned on

The LED lights bulbs in my ceiling fan all went dim this week. The lights themselves are OK because they work fine in other lamps. When I turn on the fan, though, the lights go back to original brightness. Aside from the pull cord, the lights can be controlled by a dimmer switch on wall, although the bulbs I'm using don't have adjustable dimming.

Why is this happening? I've seen issues of ceiling fan lights going dim when the fan is turned on, but not the opposite.

Upon Ack's suggestion, I did some experiments:

Initial state: ceiling fan has 3 fixtures and 2/3 fixtures have bulbs. Both bulbs are 9W. Both bulbs are dim

Experiment 1: both bulbs work at full brightness in other lamp fixtures

Experiment 2: put new 13.5W bulb in ceiling fan fixture. 1 fixture has 9W and other has 13.5W bulb. Both bulbs turn on at full brightness without turning ceiling fan on

Experiment 3: put new 9W bulb in ceiling fan fixture. Both fixtures have 9W bulb. Light dim in both

Experiment 4: put new 9W bulb in 3rd fixture. All three fixtures have 9W bulb. All bulbs dim

Experiment 5: 1 fixture has 13.5W bulb, and rest have old 9W bulbs. All bulbs bright

Not sure what's going on here.