Moving your system from the solvent back into the sink, squirt a liberal amount of hand dish washing liquid onto the base while it is still dripping wet with solvent. At this point, any remaining adhesive residue will have lost all tack.
Gently glide the fingernail brush across the edge of the base and out through the hair — all the remaining adhesive residue should slide off easily. After a few minutes of brushing, rinse your system with high pressure lukewarm water down through the base. (Repeat this step a second time)
If there is still adhesive residue in your hair system, you probably didn't soak it in the solvent long enough. Go back and repeat step 2.