Need automatic starter information. My 2009 RX350 drove without keys. 🫣

[Knutter]

I am trying to find out if an after market automatic car started could go bad & cause my SUV to drive without the keys in the ignition.  Then it didn’t want to shut off, but it did shut off by itself after about 10 minutes. Today, my battery is dead and the key broke off in the ignition. I managed to get it out. Tried jumping it with a new key fob to no avail. My question is about the location of the automatic starter. Is there a part to the starter installed on the backside if the ignition? Also, my car battery is new so it shouldn’t have died. Please help a gal out.

 

[RX400h]

It looks more like a bad ignition switch, so testing of that switch should come first. The starter contains a solenoid that receives a 12 volt signal from the ignition switch.If the switch is found to be good, then testing of the starter solenoid may likely be tested next. There may also be a starter relay, as well.
See:
STARTER. 2009 Lexus RX 350 | Lexus Parts & Accessories Online

I believe #28160 is the solenoid and 28100 is the starter.

My guess is that you will not be testing everything, yourself.