Congratulations, I think.
If it wouldn't be too rude, I'd like to re-phrase your Question. Are you saying that a bilge pump dewaters the bilge and not a drain like on many trailerable boats?
If so, yes the bilge pump needs to be operational all the time the boat is in the water unless you like to bail and are available to bail 24/7.
One question I have is: Is the cockpit self draining. In other words does the cockpit drain rainwater thru scuppers to overboard or does rainwater drain into the bilge. If the latter the boat will sink in a heavy rain without a reliable de-watering system which is usually an electrically driven bilge pump.
So yes you should trace the wiring to understand it and be able to troubleshoot it. And check the battery because many a bilge pump has soldiered on trying a save a boat but if it runs the battery down ... gulg, glug, glug.
A float test under controlled circumstances would be OK as long as you have a bail out plan (Pun not intended). Don't pull the trailer away or keep it in the slings until an inspection of the bilge is done. BTW any decent boatyard wouldn't remove the slings until a check was done.
Regarding the question "Is there a bilge pump from the factory" you can't tell. The boat is 48 years old and had previous owners. You can not assume anything about original equipment or modifications since manufacture.
You bought the boat, now it's yours.
There are three drain holes on the transom, two small side by side, which the previous owner explained one of them was where the bilge spit out water, and the larger slightly lower drain hole was from the cockpit. I will begin the search for a bilge pump tomorrow, there is a bit of wiring leftover, however most of them have been cut or tied off.
We'd have to go pretty far out of our way to get access to a boatyard to use slings (I am quite unsure of how much that would cost) we normally use a local small lake and boat ramp to float test.
We have a Deep Cycle battery we plan on using, it was from our previous boat.
Luckily the boat is sitting in the backyard on it's trailer, very very dry. I dont think she's seen water in years.
It is indeed our bought now, only up from here!