The brake lights on my 04 Jeep Liberty come on when the vehicle is parked in the garage - no one is in the vehicle and this drains the battery? What should I look for first? If I put a bungee cord from the brake pedal to the steering wheel the problem is averted but this is not the way it "should be fixed?"

Brake switch is bad. Check to see if you have brake lights. Brake switch is under the dash and it touches the brake arm.

Ignition switch may be worn out or the safety switch on the transmission linkage when it is put in park may be bad ,

kEy off?
wow both park and brake failures.
sounds like one is shorted to the other
and either park and brake are stuck.
ok take the the tests
key off, parks and headlights off,
look at all lamps on car inside and out, which are one.
is the dash lights glowing (called illumation lamps) on.
and side lights off, and front park lights off, ,yes, all off then park is off,
so of rear lights glow , is it just brakes, that means the brake lamp switch is stuck on.
elaborate please.

Do you use obd2 code scanner check the engine system and find out fault codes? How do you diagnose the Jeep?

the park unlock solenoid is operated by the brake light circuit, so what that means if u have no brake lights then the car will not come out of park, check the brake lights 1st.

I have found these shift solenoids to be a little temperamental

If you set your parking brake BEFORE you place the vehicle into park you should find you will not have this problem any longer

That is ONLY if you use your parking brake on a daily bases, otherwise do not try this because your parking brake may seize on you

check brake switch under brake pedal... if not working change it..

refer to
http://askville.amazon.com/2006-Jeep-Liberty-Sport-stuck-park/AnswerViewer.do?requestId=3458924
discussion here,
http://askville.amazon.com/2006-Jeep-Liberty-Sport-stuck-park/DiscussionBoard.do?requestId=3458924&page=1

It is located on the rear diff. at the top. The cable for the parking brake crosses close by and messes up the wiring.

Check fuses inside and underhood, as it's not uncommon for them to be on their own fuse(s)