Load drop can be caused by either the sw or the fuse connection..
So, the easy test is to simply bring a fused jumper 12v wire from battery 12V + to the lamp side of the switch..that should light the lamps.. [ you are simply bringing a NEW 12v feed to the lamps downstream from the sw.] if NO, then the connector box under the dash is suspect..if Yes, then the fuse/sw feed are suspect.
In that case bring the same jumper to the feed side of the sw and push the pedal..if yes, fuse is dropping, if NO , sw is dropping..

Sw jumper is first test I would do with your condition.

Did you try the blower???????
The reason I mentioned that is the blower would show a poor fuse connection as that would load that circuit and it is the same feed fuse for brake lamp [ as you can see in schematic]..so you are just using the blower draw as a fuse test.

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A Dalton