Hi I tried to use the relay as you suggested. At 12.6 volts the coil energizes. Could I put a resistor in series with the coil to increase when the coil energizesSounds like you have bought the perfect relay: when it is powered by a 24v source, it cuts in the 24v source. As the source is depleted to 20v, the relay cuts out to the 12v source.
Nothing else is needed.
Unless you insist on sticking to the 16v cut-out vs. 20v cut-out.