Can I safely put a 9 volt battery across 12 volt auto battery
As far as the car is concerned, when everything is off, 9V is fine. A car battery that's nearly drained will have that voltage at some point. Obviously the small 9v battery can't supply enough current to actually run any of the car's systems.
Trying to turn on even just the accessories would probably bring the little battery's voltage down noticably. So for sure take the key out before hooking this thing up, don't blink the lights etc.
As far as directly connecting the two batteries together (+ to +, - to -), probably a bad idea unless the 9V has a diode in it to prevent current flowing into it from the higher ~12V of the vastly more powerful car battery. (Under NO circumstances should you hook up &quot;+ to -&quot; and &quot;- to +&quot; !)
The &quot;gadget&quot; would have such a diode and maybe other protections. Careful to hook it up the right way. If it's an alligator-clip job, careful with that too, since all the metal parts of the car are a &quot;-&quot; terminal.