Wipers won't start up quickly.
 

When the engine is warm, the wipers take almost a minute to start working. Do I simply need a new multi-purpose relay module? Thanks in advance.

When troubleshooting problems, it is best to begin by stating the Year, Make, and Model of the vehicle in question.

This is a 1999 Grand Marquis GS. I see one available module that is simply a plug-in, and another that has 10 wire leads coming out of it.

The '99 GS wiper switch/governor are the same as my '95 GS.
You have a wiper switch assembly and a governor.
The switch is on the steering column -- the governor is under the hood.
There are A LOT of contacts on the back of the wiper switch, which may have become corroded. Removal of the switch and a cleaning of the contacts MAY fix your problem -- it's the cheapest option available, so worth a try.
A NEW switch can be had from RockAuto.com -- prices vary.
The Governor is the underhood box with the gray connector -- BIG dollars for this item !!
As of 4:15 AM MST on 5/28/17 there was ONE Motorcraft SW2518 Wiper Governor module available on "close-out" @ $23.09 from RockAuto.
If you miss that one, you might look for a used governor module on e-bay -- the price on the wiper governors is way high @ 118.79 for a Re-Manufactured Motorcraft.
If all else fails, the junk yard is a last resort.
All things considered, I would first clean ALL contacts on the Switch AND the Governor, and apply a film of Permatex Dielectric Grease to all the pins and sockets.
I found that the wiper start-up delay varies with the position of the switch -- if you turn the wipers to the "full-on" position, they start instantly. If you choose the "intermittent" position, the wipers take much longer to start.
Good Luck !!

Thanks, Merc! You're the best!

Glad to be of help, GS !!
I have completely restored my '95 GS, and am quite familiar with modifications to the suspension and drive train.
I built the car with comfortable, high-speed touring of the Southwestern deserts and the Rocky Mountains as the main objective.
Your '99 has a lot of the same suspension parts as my '95, so I may be able to help getcha goin' with some suggestions for greatly improved ride, cornering, and handling.
Gimme a holler if you're interested !!