I can't trace this back to him other than people say he talked about it,  they claim this homemade recipe can get rid of the pests for 60-80 days.

The best I could find is the recipe is about 20 years by the most homeowners in the USA. Homemade mosquito yard spray is intended for outdoor use and says it can keep the creeps away for 2-3 months. Some people make the claim it keeps other bugs away and it has a nice odor.

This recipe and applications are from MyHousePests.com. They also give Paul Harvey Credit.

1 bottle of blue mint mouthwash (you can buy any big bottle of mouthwash you like, no matter how cheap it is. For example, “Equate Blue Mint Mouthrinse”)
3 bottles (per 12 oz) of stale beer (take the cheapest – it works as well)
3 cups of Epsom salt

How to prepare homemade spray against mosquitoes

Pour beer and mouthwash into a container (an old saucepan, a bucket), stir and add the salt. Mix up the stuff properly until salt is dissolved. Pour the mixture into a spray bottle. Shake well before use.

Application directions of Paul Harvey anti-mosquito spray

Spray your backyard areas where you sit or spend lots of time outside: on decks, in patios and in alcoves around benches, on and around front porches, around pools, ponds, and fountains. If you are camping out, spray directly on the lawn grass, around and on the tents. It won’t do any harm to children, pets, flowers and vegetable plants. Do not allow anybody in the treated area until the spray is dried out. This mosquito repellent wipes out blood-sucking insects from sprayed areas for about 60-80 days.

I checked whether this is a hoax or not and snopes.com says it works