Anyhow, we resolved the issue yesterday - albeit not in the most favourable way.
Clearly, there was something wrong in the pump (i mean within the pump, motor, pressure sensor, switches, tank, etc assembly). The system worked very well after trying another used pump assembly (not sure of the term to use, but i mean the whole thing including reservoir tank).
Prior to changing the above, another mechanic had tried to disassemble and clean the pump, but it did not work. I suggested to change the O rings but they said it was ok. I also suggested to change the pressure sensor, but it was not possible.
Since i was also under pressure of time, i ended up paying for the pump (full set including pump, motor, pressure sensor, switches, tank, etc) that was working. Expensive, but it was a relief. I am keeping my old pump for future use as i suspect there is just a small problem with it.
I am relieved but not yet celebrating.