The date code on the movement says "M8" (1968), but the case date code is earlier (M7 - 1967) and I can't tell if the last digit of the movement model number is a "D" or a zero.
I've looked through the advertisements for both 1967 and 1968, along with 1970, 1971 and 1972. But I haven't found a match as everything that seems close to this one has luminous dots at each hour and mine doesn't.
I took the watch to a local jeweler for a new battery a few months ago. Afterwards, though, the watch still didn't work. They suggested that I take it to a place close by that specializes in watches, which I did. He examined the watch and told me that the jeweler put the wrong battery in and ruined the watch. Is that possible? I have the original Bulova battery but not the one that the jeweler put in.
Your watch looks to be an Accutron Calendar. I can't answer your question on the battery but hopefully one of the guys can. Not sure if yours is yellow or white so not sure on the variant.

1967 Bulova Accutron Calendar
In reply to Your watch looks to be an… by Kathy L.
Hi Kathy,
Thank you for your reply. However, the photo that you included with your reply shows a watch face that has the luminous dots at each hour, whereas mine does not. That's why I haven't found the correct model of Calendar watch.
Sue
Looks like the watch is all stainless steel.
Finding plenty of yellow gold filled and solid examples, but not a stainless steel version yet.
1968 Bulova Accutron Calendar.
The movement will take a '344' battery. This is what I use for my 218D.
It's also best to leave these movements running when not being used, unless you take out the battery. With the battery in it will still draw power (much quicker) if the crown is in the set position.
Others may have an opinion on this.
According to Darold Hanson's complete Accutron guide the stainless steel version is the Accutron Calendar "AM".

In reply to According to Darold Hanson's… by mybulova_admin
This photo also shows (and the text describes) the luminous dots and hands, which mine doesn't have...
The hands and markers are not luminous, nor does it have any luminous dots at each hour. The face is a gold color, as is the movement. Since it was gifted on the occasion of the recipient's retirement after 18 years, I assumed that the watch was gold.
Also, why would the case show a date one year previous (1967) to the movement date (1968)? Is that a common practice?
Sue
In reply to The hands and markers are… by amznwmn
It's normal for both movement and case to be the same year. We also often see a movement one year prior to the case. Though when we see a movement post case it can suggest a replacement movement or case, which often happened back in the day as services and repairs (even complete movement exchanges) were common practice.
1968 Accutron Calendar - no variant for now.
I am good with 1968 Bulova Accutron Calendar no variant.