This is a clever relay solution that would work, but so would the 4-diode solution; It's just a bit more complicated.Using two timers only requires a common SPDT 12 volt relay (automotive type) to isolate the timers from each other.
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If a relay (or anything) is going to be purchased, it should offer some benefit IMO. In post #8 I provided a different relay solution which eliminates one of the timers and one of the 12V power supplies, which could then be used for other things later.




