I did wonder if you were confused and actually, you're thinking does make perfect sense!

As John says, its the cloths/rags that people use.
When the front hairline starts lifting, but the rest is still attached, you need to lift the front and clean off the broken down glue before you can touch up the front with new glue and stick it down again.
To me, a mirror in the situation is of no use.
Instead, I would use the microfibre cloth to clean the glue away from the base.
If the glue is very soft, the cloth just lifts it off the base. Non microfibre cloths can just smear the glue around and if its a lace base, just push the glue in between the lace holes, making things worse.
If the glue isn't so soft, you can dab a bit of alcohol on to the cloth and use it that way.
Likewise you can clean your scalp too.

When it comes to a complete debond, again the cloth can be used to clean the entire base.