There are many churches in my diocese ( both large and small parishes) that have vigil lights.
Several have the standard open tray of dozens of small votives that parishioners light themselves.
One large cathedral has an interesting policy that I think could be a great option to satisfy the insurance issues.
They have about 2 dozen large votives with metal tops that look a lot like the lantern by the tabernacle, spread around the church. The candles within these are only allowed to be lit by the church staff. They have envelopes where you can request a candle lit and specify a specific prayer intention. They suggest a $2 donation and then will light the vigil light for one week for the intention. They also make it known that the church staff prays for each intention.
Also the stands these large 12 inch tall votives sit on literally looks bomb proof.
I am a professional firefighter and honestly find it pretty ridiculous that this is a fire hazard when done properly. Of course you can't drape linens and things over them or put decorations around them, but there really is no more hazard if done right then having a kitchen or electricity in the church.
I think it's just something my parish chose in my diocese. It was said when the parish was formed in the 60s that it was "the most Protestant Catholic Church in the diocese". I think this was meant to mean they were very anti traditional.
I am happy to say that it is almost the opposite of what the church is like now, like it was maybe just the times, a fleeting fad, so if that was the case it would be nice to get the lights back.
I will keep investigating but all your responses have been quite helpful. Thank you!