Thank you everyone for your replies.
I posted on Sunday night, and the rat made another appearance. He was in the fore cabin and then leapt to the porta-potti area, or back, and one time at the fore cabin he was just motionless, staring at me, but he was not too afraid of me.
I thought I picked up a rat at a notorious jetty (near an abandoned house), but this was the rakali / native water rat. As such, he wasn't interested in the Talon bait (I checked), but he did leave barnacle and mussel shells around.
So, after the 3rd time, I motored back to the launching ramp jetty and slept uncomfortably in my car. The rat could be by himself.
On the Monday, I went back to the yacht to have breakfast, etc, since he is nocturnal. I did search through all of my cupboards and underberth areas, but he'd moved. I did discover that I can close the door to the fore cabin and toilet (2 bulkheads there), such that he couldn't exit that area, but he wasn't in that area on Monday arvo.

(the floor is a teak-lookalike foam from Ebay. About $65 for 2.4 metres by 0.9 metres, and 6mm thick. Soft to walk on, non-slip and looks OK).
To get some epoxy out from under the cockpit I saw his tail and foot stuck in the corner of the vertical slides and the bilge:

His black and white tail is on the left, and his foot is next to the small styrofoam on the round inspection port. He was stuck, facing downwards.
I thought about grabbing him with my leather gloves, but he'd be vicious and angry. I then tried to catch him with my fishing net, but thought he would run too fast and go anywhere in the yacht. But after a few minutes of him being stuck, he ran under the floorboards/bilge area. I sealed him off and thought about the net again.
In the end, I opened the seacock and drowned him.
This morning I fished him out and then tried draining the bilges. The bilge pump blew 2 fuses, so I had a look at replacing the pump. (I wired it up last time but thought that it wasn't working well). I discovered that he chewed through all 3 wires of the bilge pump, and shorted them.
End of story. I thought he was too big to wrestle with, and to chase out of the yacht would have been difficult, unless I could corner him somehow.
He came in through the opening of the outboard well (leg), so I will seal that better next time aboard.