Reddit mentions of Automatic PRO AUT-350 Connected Car OBD II Adapter, Realtime Car Tracking via 3G and No Monthly Fee, Trip Tracking, Engine Light Diagnostics, Severe Crash Detection and Alexa Skill.

Take a look at this one

Automatic AUT-350C Pro Gold 3G Connected Car Adapter https://www.amazon.com/dp/B01JRBQ9PC/ref=cm_sw_r_cp_apa_5egrybRD4G45G

No fees or sim card needed

Not a complete answer OP..

But I got one of these when I suspected my ex of cheating:
Automatic AUT-350C Pro Gold 3G Connected Car Adapter https://www.amazon.com/dp/B01JRBQ9PC/ref=cm_sw_r_cp_apip_uAAYEAqunJTtg

Just wrap it in electric tape, taps right into the OBDII port and with the tape you can't even see it. It shows travel time, destination address, and I could even use the 3G to look at location real time. Works flawlessly and I actually still have it in case the car is stolen. The accompanying app is a little rudimentary but it has everything you need, and you can even tie it into IFTTT if you want

Edit: since I saw another response, this is $130 or so but requires no battery or monthly plan. It uses 3G cell towers for all the information. Since everything is 4G and up today they don't even bother with a plan

Here ya go: https://www.amazon.com/dp/B01JRBQ9PC/

As far as uploading to a private cloud, that would be a bit more difficult. You could probably set up a server to forward the data to a private cloud, but it'd still be on their servers first.

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To DIY a solution, you're talking about a bluetooth dongle with some sort of cellular-activated IOT device, AND a GPS puck/receiver, plus the private cloud you'd set up separately. Do-able if you're looking for a project, but definitely more expensive both time and money wise than the bought solution (the GPS alone is ~$50, add an OBD dongle and an RPi and you're over-budget already). If you're trying to do pre-96 cars, that's a LOT of custom wiring, due to the lack of OBD2 (and I'd know, because I went through all that to datalog my '94 MX3).

Edited:
copied from amazon description:

Automatic Pro is an adapter that plugs into almost any car to provide unlimited monitoring with zero fees. Know where your car is at all times, make sure that in the event of an accident that you and your family will be taken care of, and even connect your car to your Echo, your smart thermostat, or any other part of your digital life. This product works only in the US.

https://www.amazon.com/Automatic-Connected-Realtime-Diagnostics-Detection/dp/B01JRBQ9PC

Tangental information: this sounds a lot like the "Automatic" device, though there are others this info might be useful to you:

Automatic AUT-350C Pro Gold 3G Connected Car Adapter https://www.amazon.com/dp/B01JRBQ9PC

This one. I got it for Christmas and I've enjoyed the tech side of it. I think you can download 3rd party apps to use more of the technical things. Technically the chip can read everything about the car and Automatic's app barely shows you any of that. I've never had to use the built in crash monitoring, but it's nice knowing it's there in case I'm unable to call for help.

What about this device?

Automatic AUT-350C Pro Gold 3G Connected Car Adapter https://www.amazon.com/dp/B01JRBQ9PC/ref=cm_sw_r_cp_api_lw65yb4890EAH