2015 Prius C - P261B code

Hello,
My 2015 Prius C (in Canada) shows the check engine light. The OBD reader says : P261B engine coolant pump b control malfunction.
The check engine light has been there on and off (2 days on 1 day off, sometimes 3 days off) for more than 8 months now, and I've been using the car with no issues. Only thing is that 4 months ago, I got a Check Hybrid System warning while I was driving. I immediately stopped the car, unplugged the battery box in the front, waited 2 minutes, plugged it back and drove off. No issues since, but always the check engine light on and off.
Last week, the "Check Hybrid System. Stop the vehicule in a safe place immedistely" came up while I was driving. I continued to drive looking for a spot to stop as I was on a main way. I felt that the accelerator is not working, the car is just losing speed. The car stopped I was lucky enough to stop on the side of the road. I did the same thing as before (unplug the battery box, waited 1 minute, then plugged it). I drove off with no issues. Next day, the same Check Hybrid System message came up and again the car stopped on its own.
I used my OBD looking for any codes but nothing except the P261B fault code. I used the Dr. Prius App to do a Hybrid battery test, it gave me 77 % battery health. While doing the code reading, I erased the codes through the Dr. Prius App (I already did that few times in the past).
The next day, I took the car to a mechanic nearby and told him that it needs a coolant pump replacement. He said they need to make their own diagnostics before replacing anything. I left the car in the garage. 2 hours later, the garage called me saying that they did their diagnostics but they could not find any fault codes on the car and that it is working well, except that the 12 V battery needs replacement (an issue that I noticed recently). I went to meet the mechanic and I showed him the fault code I get each time I use my OBD reader. He said that we should then replace the coolant pump. I asked him for an estimate, he said its around 1200 CAD for the pump and the battery replacement all included.
I took the car back and I used my OBD reader looking for the fault code, but NOTHING shows up. I even used another OBD App and it also did not detect any codes. I know that even when I erase the codes through any App, the code still remains, but this time the P261B code just disappeared.
2 days later, the check engine light came back. I used my OBD reader and it showed the P261B code.

Now I'm wondering, is the P261B code actually linked to the "Check Hybrid System. Stop the vehicule in a safe place immedistely" warning I got??. I also wonder how come that the code disappeared from the car for few days and did not even show up on the advanced diagnostic tool of the mechanic??
Also, looking back at the code being there for so long with no real impact on the car, does the pump really need to be replaced, or is it just a sensor/wiring issue that needs to be fixed??

Any comments will be appreciated.

 

@ChapmanF, Thank you for your explanation and advice. Much appreciated!