Not that I'm paranoid, but ... it might even be possible to track phones that have been turned off / powered off. A trickle charge could (potentially) allow the recording of location data every few minutes and store it. When the phone is powered back on, the stored location data is there to be tracked.  
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In the old days, you could just remove the battery from your phone to block that sort of stuff. Today, more and more phones have batteries that cannot be removed or replaced so they can be Always On, even when they are Off.  
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What's next, microchip implants?  
http://en.wikipedia.org/wiki/Microchip_implant_(human)

In the office , car, home, etc .  

Obviously not ideal, but if you need to, might work for shorter appointments.

...in terms of using the proposed app for contact tracing...and we all believe that, right?

And even more so when some of these politicians decide that "in the name of public safety" the use of the app will become MANDATORY (hmmmm....starting to sound like China, right? ).

I'm sufficiently nervous any time Google and Apple want to cooperate on something like this, but when you toss in the natural inclination of any politician to grab more power and restrict the rights of citizens (especially in light of "never let a good crisis go to waste"), it's got me truly concerned.

Separate phone that you use once and toss in between any session sounds like the only way to be relatively "safe" from this kind of intrusion.

Anyone else got a better solution?

Honestly, even with these new contract tracing apps... They have been silently following you and tracking you. So do the apps bother me? Honestly, no.    

When I would get very worried is if there is a data breach and non authorized people are now able to track you or even worse, trace people who you were in contact in the past x minutes, hours, days, etc. What I mean by this is, if you go out on a date with a client or provider, maybe they can figure out which phone was closest to them during a certain time frame. Then when they leave said client or provider can trace where you're going, etc.

If you can still find a flip phone thats the way to go for hobbying. cheap, use tracfone minutes and only for hobbying. Any sign of trouble just tosh it or destroy it. i own 3 of them cost 5-20 dollars can only call  and text, some have a poor camera.