For a cover to use on the Bulldog Powered Drive Trailer Jack # BD500199 referenced in your question, I recommend the Ultra-Fab Protective Cover for Electric A-Frame Jacks # UF38-944020. This will easily slip over the jack and can be secured using the drawstring. This cover measures 12 inches x 14-1/2 inches. I have attached a video demonstration of the cover for you to check out.
There are several places water can get into any given jack. Water should be able to drain out though. If the exit points which would be at the lowest point are clogged then the water would not be able to exit. You could use a jack cover like # UF38-944020 for future use. There is no telling how much damage is really done. If there is enough corrosion then something inside could be structurally compromised and fail when you have weight on the jack. I would not be comfortable offering...
If a trailer didn't have a trailer jack, this means of transport would be pretty much useless – unless you are strong enough to lift it by hands or hitch (unhitch) a tow vehicle somehow else. Jacks can be manual and electric. With the help of an electric jack, you can hitch up substantially easier than with the manual unit, since a manual jack requires the application of physical force. Anyway, whatever the trailer jack you have, this part has to be completely workable and sufficiently reliable to prevent troubles during a journey under various conditions.
Quickly and easily install a 4-way trailer connector on your vehicle with this custom harness. T-One connector plugs directly into OEM tow package wiring harness - no cutting or splicing required. Features: Provides a 4-way flat trailer connector at the back of your vehicle to power your trailer's signal lights Designed for use with a factory tow package Compatible with 5-pole, 6-pole
I went out to the warehouse to look at the Lippert Electric A-Frame Tongue Jack, # LC285318. In order to remove the screws that secure the cover you will need a long and thin phillips head screwdriver. If you don't already have one, you'll want to purchase a Protective Cover, # UF38-944020, to keep your jack dry when you are at the campsite. This will protect the head of the jack and keep the motor protected from the elements.
This custom-fit mount lets you secure your Hi-Lift jack to the passenger's side of your Jeep. The jack mount lock codes to your ignition key. Automotive-grade, weather-resistant black powder of keys - for your hitch lock and coupler lock, your pickup cover or trailer door, and all the various padlocks securing your equipment? Tired of fumbling for the right key or having to replace a lost key?
Use this electric tongue jack to lift your trailer with the flip of a switch. The sturdy steel jack can handle up to 5,000 lbs. It has 18" of travel and a 5" drop leg for extra lift. LED Features: Electric jack with 12V motor lets you lift and lower your A-frame trailer quickly and easily Top-mounted toggle switches are easily accessible Large LED side lights make it simple to set