There's not a lot that can be done through the rear panels except inspection. It sounds like either the brake isn't properly adjusted, it's oiled/greased up, or the clutch needs adjusting. If it's oiled up, it can be washed. I'd use kerosene or diesel, NOT gasoline to do the deed. Remove the upper plate so you can see, then fill the compartment 'til the lower part of the band is covered. Drive it back and forth a bit, using the only brake occasionally, then drain and let it sit for a few minutes. Leave the cover off and run it back and forth again while "riding" the brake gently for a minute or so at a time. That should dry it out. If it's badly oiled up, you may have to repeat the rinse and dry a few times.
Those compartments need to be checked and drained occasionally as oil, grease and dust can build up in 'em.