Brake actuator running when sitting in park

Sure. Possible.
But the brake pump running is NOT a sign of a weak 12 V battery.......because the 12 V is charging when the vehicle is running.

 

You've asked the right question, and given yourself most of the right answer. The pressure is what determines when the pump runs, and for the pump to run cyclically like that, it can only be that the pressure is not being held. That isn't something your 12 volt battery, for example, could be responsible for. It's a plain matter of mechanical/hydraulic sealing.

In a fresh actuator where all the valves are still tight, the pressure can hold up for some hours, if the brake isn't used, before the pump has to run again.

That doesn't stay true forever in old actuators. They wear out eventually. That probably isn't related to the work you did at the calipers. Did you press the pistons back in at all for any reason?

We frequently see posts around here from people who have put off dealing with the issue until the pump is running every several seconds with nobody touching it. At 4 to 5 minutes, even though that's already a whole lot worse than a shipshape system, you've got more of the luxury to take some time deciding what to do about it.

 

You already in post #1 correctly pinned the behavior on pressure not being held. The mere presence of air somewhere will not explain the behavior. Fluid that is being moved into the accumulator by the pump is clearly moving out again, over and over. Only an internal leak gives you that story.

When you pressed the pistons back in, did you have the bleed screws open, so the old yucky brake fluid in the caliper could escape, and then top up the reservoir with fresh fluid? Or did you have the bleed screws closed, so the old fluid got pushed back upstream into the actuator?

 

On the off chance that you may have pushed some gunky fluid backwards into one of the actuator valves, you might pick up a pint or two of fresh fluid and run through the long-form brake bleed procedure (there are two choices in Techstream, the longer one is shown as "after actuator replacement" or something like that).

The long procedure works a lot of the valves in there and blasts pressure through them, so it might flush out any gunk in a valve for you. That could be an explanation of how you'd have the symptom at 70k, which is pretty early for any of the valves to just wear out.

In any case, it doesn't cost much to try, and beats replacing the actuator if it does the trick.

That pushing piston back without opening bleeder practice is one of those low-risk-of-problem, high-cost-of-problem deals. You can do it oodles of times with no problem. People who've done it oodles of times with no problem will regularly chime in "oh pshaw, I've done that oodles of times with no problem", which is swell, until you're the guy having the other experience.

 

Like air sneaking into the cylinder while its bleed valve is open? I'd worry about that possibility.

 

Even if that happens (as unlikely as it is, while you're creating positive pressure by pushing the piston back), the most it costs you is a quick brake bleed of that cylinder (the simple kind people often do without a scan tool).

I typically start, anyway, by attaching a tube to the bleeder that runs (at first) upward, and already has fluid in it. Even if you momentarily create a negative pressure in the cylinder, what gets sucked in is the fluid, which you see happen.

Your possible cost from forcing gunky fluid back to the actuator is an actuator. That's a different world of hurt.