You should disconnect the negative on the battery when working on the TIU, any electrical work (other than testing) for that matter.
If you do choose to test the TIU this way, it would be the easiest for your situation.
Remove the two screws holding the TIU and turn it around. Don't remove the wires. You will need a flat screwdriver and plyers to pry open the tabs and remove the cover.
Once you remove the cover and fit the TIU back in its place the back side of the circuit board will be visable. That is what you spray with electrical cleaner. Just turn the ignition off and spray it for about 2 seconds and wait a minute or two for it to evapourate and cool the TIU. Then try to start it.
If you buy a can with one of the thin tube nozzles you can lean over and spray it from the drivers seat. See photo for sets to take removing cover. You won't need to remove the TIU like in the photos.
Contact cleaner I used, but any contact cleaner spray will do.
http://wd40specialist.com/products/contact-cleaner/
I think you need to varify the Starter fluid test is not working before you move forward.
I know everyone has their tried and tersted methods for testing. I found spraying it down the air cleaner for 2 to 4 seconds while someone tries to start the engine works fine.