When you do this please post what and how you rerouted the wires to accomplish this
To get engine running hours
You wire the hourmeter to the + wire on the alternator .
Check that this wire shows 0 volts with the key off and with the key on but the engine not running
This can not be done on Kohlers as their rectifier needs to be powered so the + wire is hard wired into the battery.
To get the deck running hours take a feed off the PTO wire.
This is what most do so you end up with cutting hours , not engine hours.
Again if the PTO is left on you will clock up phantom hours.
After that it gets a little complicated because the only things that are dependent upon the engine spinning is the alternator.
But the rectified circuits have switching diodes in the regulator so the + rectifier wire is rarely 0.
So to work out when the engine is running you need a device to measure which way the current is flowing through the alternator wire and then trips a relay to turn the hour meter on.
Can not remember their name but they are readily available from the electronic geek shops a simple circuit just a couple of diodes and a switching transistor.
There is an ampeter that has one in it, hit the market a few years back but flopped because the cost benefit of using one was pretty low.