you need to prime the pump for CTS-Coolant Through Spindle.
Ussualy the pump has a hole covered with a "cork".
take out the "cork" fill in some water untill is full and than start the pump.
WARNING!
Never run CTS without running the spindle.
if you wanna check the pump first start the spindle with minimum 500 rpm and than you can check the pump
yes should be
the pipe that comes from the pump should go first in a distributor that has also an air pipe in it .
that distributor has safety valve for not letting the water go in the air and the air to go in the coolant.
I made a rapid sketch
I never took off because was never broken.
my suspicios is that the pump has not enough pressure to open the spring on the safety valve.
can you insert a gauge on the coolant pipe and check the pressure leaving the pump?
normally must be 10 bar or so.
or take off the pipe from the distributor and try to put in direct on the rotary joint---only for testing to bypass the valve.