A good trick to make removal easier is to put warm water on the eggs for. Few seconds.
Warm water tricks the eggs into thinking the horse is licking and they will release themselves easier from the hairs. That is why they don't wash off with rain, rain is cold:shock:
Also, allow me to make your bot day even better lollol.
There is such a thing as Throat Bot flies. They lay eggs in the jowel area and those little soandso's are able to self-migrate into the horse's mouth:shock:
You just about have to pull the jowel hair backward, pretty tight, to see them and they are even worse to get off the horse. I smother them and their travel path with any kind of ointment. Hemherroid ointment, antibiotic ointment, any ointment safe for a horse. I also keep all that jowel hair shaved close to the skin so I can find them easier.
I don't shave feeler whiskers, just the hair where the eggs can "hide in plain sight":-(
I second the suggestion of the lava stone. Blackish rectangular thing. You can also find them in the cleaning items department of many stores...some farm supplies, maybe WalMart, Lowes, etc.
I hate bot season!