If you are in the Apple ecosystem, you could get an Apple Watch with cellular. That can be tracked with Apple’s Find My. You would have the initial cost of the watch and probably $10/month for the cell connection. Added bonus: it has automated fall detection.
Where can you get a cell phone plan for only $10 per month?
Most all cell carriers charge $10 extra for an Apple Watch cellular to be on the phone’s plan. This could be attached to your wife’s cell plan. Not sure about cellular-capable Android watches.
Wow! $10 a month for a watch GPS locator that does nothing else. I might need it 3 times a month. No thanks. Had no idea people spend as much for cellular service as they do.
The $10 a month gets you much more than tracking. It provides full access to all of the watch’s online functions for those with a watch not carrying their phones. But I can see where that’s a lot if you’re only using it a couple times a month. For example, you can send and receive emails and text (iMessage) messages without having your phone with you.
There are many other trackers out there made for dogs and kids. But I don’t think you’re going to find any with less than $10/mo subscription cost for the cellular connection.
As mentioned above, Apple AirTags are free after the initial cost ($29). But they rely on being within bluetooth range (about 10 meters) of somebody with an iPhone. It doesn’t have to be your iPhone or anyone you know, but you do need to be near some iPhone. So if your need would be satisfied if the signal only got to your wife when you are near people that have iPhones, then an AirTag might satisfy your use case.
For a point of reference on cellular costs, Clark recently mentioned that Visible now has annual plans. Regular Visible is usually $25 a month plus $10 extra for the watch cell service. The new annual plan for Visible+ (higher speeds, etc. than regular Visible) is $395 and includes the watch cell service. This works out to $32.92 a month. I just switched my service over to that.
Get an apple watch and put you patient’s appointments on it and charge it to your dental practice expense. 
Excuse my ignorance.
So my wife could have her I-Phone at the house, and I could be out on a bike ride miles away, and she could track exactly where I am?
And I could send her messages from the watch like “I am stranded on Minnix Road, could you please pick me up in the truck.”?
And if we are separated in some city we are visiting, the pair of devices would help us find each other?
Yes the latest Applewatches contain 5.6 billion transistors, 32GB of memory and a four-core processor and can communicate over bluetooth, wifi or lte cellular networks.
Yes, all correct. You need to make sure it’s an Apple Watch model that has cellular radio (not all of them do). And you have to pay the probably $10/month subscription for the watch cellular connectivity.
How it would all work would depend if you each have your own AppleID or not. That is, if you each have your own iPhone.
For location tracking, it wouldn’t really work much differently if only she has an AppleID.
For text messaging, it would still work if only she has an AppleID, but the messages would appear to be coming from her and sent to her.