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Pete, thanks so much for your answer. I would caution, however, that flight immediately following such a restart is not advised and may even be against regulations. Setting aside the regulations, let me suggest a couple of things before taking off.
First (and this is subject to Pete being in accord), I would check water level in the cells and add distilled water before jump starting the rear engine.
Second, I would run the rear engine 5-10 minutes after disconnecting the jump (external) battery and then (gasp!) turn it off to see if the battery accepted some charge. How close is the battery voltage to 24 volts with the master switch on (so that there are some loads connected). If there is no voltage meter on your panel, measure the voltage across the aircraft battery posts with an external voltmeter. You might also turn on some heavier loads (lights, maybe flaps, but not cowl flaps due to their sensitivity and cost) and see if the battery has juice to operate them. The purpose of this step is to determine whether the battery had drained down to nothing but is good (i.e., will accept a charge) or is totally gone, incapable of charging. Don't you want to know this before you get going? Even if you have to take off (after re-connecting the jump battery and following Pete's procedure for restarting both engines) don't you want to know whether there will be a) some or b) no battery on board? For instance, if you lose an engine or an alternator. Or, in my 337G, with a powerpack for the gear, I know my gear will hang up in mid-travel when there is little or no battery left (because the last few seconds of gear travel demands so much power that the alternators alone can't hack it), so, if I choose to go, I'm going to leave my gear down.
Third, once I have both engines going, look at your idiot lights to make sure that both alternators are putting out. I wouldn't take-off with a bad/dead battery and a bad alternator. If your idiot lights are bad or unreliable but you have a voltage meter on your panel, you can determine alternator output by looking at the meter as you turn each alternator off and then on.
Finally, depending on your findings as to the condition of the battery and the alternators, it would be most prudent if you had a hand-held aviation radio on board before take-off.
Ernie
(Sorry if the above was too obvious/detailed/pedantic for the savvy -- it's meant for the average owner or pilot.
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