Posting some pictures of your setup might help us give better answers to what might be the issue.
From what you told us, there is one possibility that might cause the puddle to leak and then not leak. Since I can't see your setup, consider this a generic answer as I have seen this on any connection using a swivel fitting in an RV setting.
At the piping ends of most RV style water pumps are swivel fittings to allow you to screw the hose or piping onto the pump and not have to spin the pump to get them to go on. Many of those fittings are in the PEX style family of swivel fittings. The fittings look like this, your brand might be different.

On the end of the fitting is a cone washer, look like this,


This is the cone washer by itself as a replacement from Flair-It company.

Those swivel fittings sometimes loosen up and drip. Sometimes the cone washer was jammed sideways when installed and did not seat right and they drip. When the camper get old, like 10 plus years etc. the washer gets a little brittle some times and being compressed long enough start to drip.
Assuming your pump has a fitting similar to the ones I showed above, first just try and tighten the fitting. Most times that stops the leak. If that does not stop the leak, then change out the cone washer.
Now showing up on newer water pumps they have swivel fittings with no cone washer, they use a plastic nut and inside the fitting wedge cone to create the seal, they too can leak if they are loose. There is no cone washer to replace, but the loose fitting or a damaged wedge cone can leak. The fitting looks like this from Shurflo
https://www.amazon.com/SHURFLO-244-2926-Straight-Wingnut-Adapter/dp/B002IZJ7CW/ref=asc_df_B002IZJ7CWI find it helpful to put dry paper towels under a suspect leak area. The monitor it often, and have the pump on to pressurize the system. If you catch the drip in the early phase of the leaking, then you can see where on the paper towel it dripped and help back into where it came from.
You did not say if you were on city water or only using the pump and fresh tank. Pump leaks can happen from both water supply areas, but city water hookups can have very high water pressure that can aggravate a fitting leak more then the onboard pump can. Have you noticed this problem more on city water or using the onboard pump?
Hope this helps
John