Primary Battery & Coolant Pump issues

it's getting down there. hard to say how much life is in it. you could get a load test free at an auto parts store. they also carry batteries.
there's no consensus on the best battery, because there's no testing. i threw in another oem for $200., even though pep boys had one on sale for $150.

 

Driver's side, right? The inverter coolant pump is down there, but it should be running constantly, just not making much noise. Check the coolant reservoir next to the inverter when the car is in IG-ON mode (2 presses of the Power button, without your foot on the brake.) You should see movement (some say "boiling") in the coolant in that reservoir. If you do, the pump is still functioning, but if it's making noise, it might be on the way out.

Other than that, there is a pump in that same area that fills the Coolant Heat Recovery Canister (thermos) which does make some noise, but that should only be evident for a few seconds after the car shuts down.

What I suspect you are really hearing is the brake actuator/accumulator, which is more toward the center, next to the firewall. It will normally run for a few seconds upon entering the car and then sporadically as you are braking, but only in intervals a minute or 2 apart, if it is functioning properly. If the accumulator is leaking, however, the actuator will start running much more frequently, a few seconds apart. That means trouble. The part is quite expensive if purchased from the dealer, but the labor charges to replace it are what will really kill you. If that is indeed what is making noise, you will eventually see the ABS, VSC and Slip Indicator lights glowing on your dash. At that point, you will need to do something or possibly lose braking function. Your best course of action would probably be to look for a used part at a wrecker and hire an independent shop to replace it.