Right so, here are the photos, as you surmised there is what looks like a
View attachment 470507View attachment 470508View attachment 470509grub screw, the smallest allen key I had with me was 10 which is too big
Oh wow , i was right to check the tap type , and yes that is a small grub screw . I'm afraid that's not the same as the one i worked on , but with that said , logic dictates the layout should be pretty much the same . Just be careful as you move forward and be prepared for the unexpected . I have another assumption , but it is purely that , again based on logic . I tend to think outside the box a lot nowadays , sorry .
So what i would expect to see , is the cassette in the base , like this one

, now straight away , be aware mine was held in place by a lock nut like this .

. It was a bit of a challenge to get at , but i finally succeeded with a pair of long nose pliers . Now i'm gonna throw another caution in here , mine appeared to be made of a soft brass , and was slightly damaged during removal . It didn't affect the tap going back together , so i strongly doubt it will have any affect on the tap operation itself .
Now the bit we are interested in , is the microswitch , and frankly i would expect to find that under the tap head . The motion of the rocker function activates , and de-activates the pump , and as it's a simple idea i wouldn't expect to find any different . So on that note , and to give you some idea of what your looking for i'll post what i found

to help ya out . Now unfortunately i don't have a fully assembled picture of my tap , and the new one is in the garage (yep still yet to fit it) , This is the actual body , with the faucet disappearing upward's . There are two ways the switch could be mounted , clip in , to the actual rocker as on mine , or screwed to the main body as was the case , with the guy who was advising me .
Now my assumption , well i'm gonna stick my neck out a bit here , i think your tap is one of the older designs , and with that , i suspect the rocker top will just pull off . Unlike mine your legend is on the side , and the screw has to be vertical That would lead me to suspect your micro switch is likely screwed in to the main body instead . However before you even think of following my logic , just remember i've broken one tap already , so go carefully . On the other hand , it maybe some time since this job was last done , so it may be stiff anyway .
I'm gonna post just one more pic , and that is of the part i broke ;

This is the top of my tap with the water temperature legend , and the screw hidden under . Your legend is on the side , and it is that , that leads me to the assumption i made of your tap .