I have some rim fire specific bore solvent ( Bore Tech rim fire blend) but I haven’t proven it to be any more effective than my other solvents. I personally use only nylon brushes in conjunction with Iosso bore paste on my rifle bores, but you may have satisfactory results using other methods.
If you are up to it, a complete disassembly and clean may be appropriate for your “Gill Gun”.

Dodging lions and wasting time.....