Can you post a good photo of the board Ian? It may be possible to work out where the wires go from that. I think from your description it's only the switch wires that have come adrift, not the three speed-control wires connected to the pot?
How to post photos on the forum here.
This circuit pinched from Amadeal's CJ18 Manual may help, assuming your lathe's electronics are as described in it (mini-lathe electronics vary a fair bit, similar rather than identical):

The red square highlights the 3 speed control wires marked P1, P2 & P3 connected to the potentiometer. These connect to board KBIC240. I believe the board should have 3 tag connectors arranged in a triangle (as shown inside red circle).
An oddity is that the reversing switch (marked SH-A) also has a connection marked P3. (inside Orange Circle) I don't understand this; the photo might help.
The switch part of the potentiometer (inside blue box) has three wires, 2 of which ( 'TA' ) are connected together. One of these (doesn't matter which) goes to a terminal on the Reversing Switch; the other goes to a terminal on KZSHUXBOARD as does the third wire 'TG'. TA & TG are highlighted by a blue box.
Amadeal's drawing probably indicates roughly where on the real board the terminals are to be found, and they could also be marked more-or-less sensibly on the board itself. May be terse abbreviations!
Hope that helps.
Dave
Edit: pesky smiley removed
Edited By SillyOldDuffer on 04/03/2019 13:35:01