Interesting question! Permissible pilot maintenance is covered in Far 43.
Brakes are not mentioned in Far 43 Appendix A. Preventative maintenance. However to accomplish items (1) - (4) (landing gear and strut maintenance) on most aircraft, one is required to remove the brakes. I would assume that one would be permitted to clean an verify the fit and correct operation of the brakes prior to reassembly. As long as it DOES NOT INVOLVE COMPLEX ASSEMBLY. I see this as an opening... "Well I got it apart, now I have to put it back together. If I put it together, I am responsible for making sure it is working/adjusted right. If it becomes COMPLEX, I will have a mechanic help me."
On Pipers the pilot checks and fills the brake reservior on preflight. Obvious conclusion: If the task is specified on a manufacturers checklist or other "official" document, it is permissible. Since we are on the RED BARN, I am guessing that we are concerned with a vintage aircraft. I would look for any of the old time instructions that came with the aircraft: operating manuals, handbooks, TCDS. If you can find the item on a pilot's preflight, postflight, turnaround or daily list, then it is a pilot function.
Some of these functions apply to military A/C, bit if the pilot was allowed to do them on a X/C, then you would be also.
CAVEAT>>>> I am not an expert here. Just giving an opinion. So, if someone else feels different.........