PaulC,
Had a few minutes tonight so I dragged out the original drawing and modified it for you to your new design and specs.
You might want to check it out......
BTW..... most hall effect are open collector and require some kind of circuit to the positive rail be it either a resistor or an LED/resistor otherwise they simply just won't work.
It's just signal level stuff so 1k0 is ok.
I have shown it with a 680R as i calculated it out with a red LED @ 20mA.
Good for setting the timing.
The original KY-003 already has a pullup so the 680R and the LED in this instance if using that module , is unnecessary.
If using a bare hall effect such as the 3144, always good idea to wack a small (0.1uf) cap right on the switch terminal legs power rails.
Not my idea, rather Allegro.
For others, just take note the order of the pinout on the KY-003 will be different to that shown above so don't blow it.
It might be an improvement to add a small series capacitor in the signal lead between the signal output of the Hall Effect and the BC558 base resistor. That way, the transistor only turns on during the pulse from the hall effect rather than being on all the time when the hall effect is on. (e.g. engine stops)
One of those suck it and see things I guess, might be unnecessary as KISS is best in many instances.
Finally a link to your reed switch.....
12V SPST Low Cost Reed Relay | Jaycar Electronics
dsage..hope this helps....
Cheers Jorgo