Try some button combos like...Alt-f Alt-n Alt-m , i think for qualifying to work you have to be sat in the garage looking out and they try the above button commands , try other Alt-? combos too when looking out of the garage as i know there is an issue with something not being displayed until you do 2 Alt-? button commands but it has been a long time since i used tvstyle so good luck
Just tried a "RF1_TEST" tvstyle profile that has a live timing monitor which is what i guess you mean by the live qualifying time.
Pressed Alt-a to toggle the plugin "on" then needed to press ALt-N to put the live qualifying monitor "on"..this disables the other onscreen meters and displays a monitor style image with the live timing screen, Alt-N toggles the monitor off and displays things like the rev counter again.
And i did this from the garage looking out.
Open the tvstyle profile folder and find the profiles folder and see if you have a "Monitor.tga" texture, if not then you may need another tvstyle profile!!
Good luck.