Knowing me, I would probably just tend to do what I see other people doing, although I would prefer to understand why I am doing it. In this case, I assume it is a gesture done out of reverence to the Lord
Correct. Christ is truly present in the Tabernacle. He’s there.
If we were to see Him face to face, we would certainly genuflect, bow, and maybe more!

Peace Tommy!
We do reverence the altar by bowing, because that’s where the sacred sacrifice of the Mass (the sacrifice of the Lamb of God takes place.
Tomorrow is the Mass of the Lord’s Supper. At each parish there is a single Mass commemorating the Lord’s Supper, and then follows a period of Adoration in a separate place, called an “Altar o Repose” to reflect on the time Jesus spent praying the Garden of Gethsemane. It’ a time of silence and contemplation on the Passion.
This might be something you 'd enjoy going to (the Triduum liturgies) as you contemplate the faith.
If your family is not comfortable going to Mass, you can always go to the Veneration of the Cross on Good Friday. There a liturgy of the Word, followed by Veneration of the Cross, where the faithful walk up to a crucifix (some parishes use a rough hewn cross…I’m not going to get into the annual debate of cross vs. crucifix) ) and they go up single file and kiss the wood of the cross.
It’s very moving and I think people of all faiths get a lot out of this service.
The local parish will also have Stations of the Cross at 3 pm, the hour of His death, typically.
I believe Jimmy Akin has much out there right now regarding the various Triduum liturgies. You may want to look at those articles.
Peace Tommy!