Hi. We have two ground central air conditioning units. Our electric bill last summer maxed out one month at $375, and we live in a single story home with 2 x 6 construction so it's fairly well insulated, but we were shocked at the high electric bill. I was working at the time, so I was trying to only run the air conditioner conservatively to cool the house. We just moved into this house last summer. This year I am home a lot more since I was laid off from my job a few months ago and noticed that the air conditioner blower doesn't seem to be turning off enough. Even if it has reached the desired temperature, the fan blower is seems to stay on. I have the fan set to "auto" mode (not the "on" mode).
I have taken the face plates off both thermostat units for comparison wondering why this fan is constantly blowing on the main or larger a/c unit. Here are the differences in their settings (the larger unit is the one I think we are having the issue with, so I will try to be as clear as possible describing the differences).
SMALL unit thermostat wiring & settings: All of the colored wires appear to be installed in the correctly labeled spot. The thermostat is selected for "gas or oil".
LARGE unit thermostat wiring & settings: All of the colored wires appear to be installed in the correctly labeled spot EXCEPT for the green wire, which is connected to the "O" spot instead of the "G" spot.
***The thermostat is selected for "electric or heat pump".***
We asked our neighbor, who has the same models of thermostats and a/c units that we do if we could take a look at her wiring and heat settings to their two thermostats. Both of their thermostats wiring diagrams are set with all of the wires appearing to be in the correct spot, and both are selected for "gas or oil".
***We do have gas heating systems.***
My husband is a very handy and knowledgeable person when it comes to wiring something, but we don't have experience with the air conditioning/heating units.
He is comfortable making the change, but would like confirmation that we should move the green wire to the "G" spot behind the thermostat faceplate and switch it to "gas or oil".
We live in the hot desert southwest if that is helpful.
Bryant is the brand of a/c units outside.
Honeywell Model TH4110D1007 are the two thermostat models we have indoors.

How was your neighbors green wire connected? Not always connected the same but green is in many cases fan relay. Considering the location and not knowing your solar load, which must be very high unless you are well shaded, $375 doesn't seem out of line. You have 2 units so you must have some fairly large square footage. If the system is piped through the attic, the ambient heat load is tremendous and regardless of size can only cool so much.

Thank you for your response.
Our neighbors green wire was connected to the "G" spot/connection. We have the same model of home (about 2800 sq. ft.) as the neighbors house we checked.
Do you think we would be safe to select the "gas or oil" selection and move the wire to the "G" connection?
Over the last few days, I made note that the air conditioner fan never shuts off unless I manually turn off the air conditioner. For example, if it reaches the desired temperature setting, the fan stays on and keeps blowing instead of shutting off like our other smaller unit.

Considering that your neighbors was connected to green, I would try.

Here is a link to the installation & set up manual for the stat.
https://customer.honeywell.com/resources/techlit/TechLitDocuments/69-0000s/69-1928EFS.pdf