I am still trying to nail down exactly which model yours is, but it is indeed a Shimano Bantam Beast Master. The toggle arm indicates yours is a two-speed reel. What was throwing me off was the AR on/off switch on the top of your reel.
Shimano made this same reel in the Bantam Black Magnum series, but eliminated the AR on/off switch, but is essentially the same reel. And in 1990 Shimano made your reel again as the Bantam Beast Master VR and again eliminated the AR on/off switch.
So according to the Shimano book, your reel is either a Bantam Beast Master III, or a Bantam Beast Master V, both were made only in 1989. (Your reel has both the 2 speed lever along with the AR on/off switch. A more rare combination.)
These reels were the predecessor to what would become the Bantam Curado reel just a few years later.
So the model numbers for your reel is either a BBM III, or a BBM V, both designed in 1987-1988. The schematic was drawn up in October of 1988 and your reel was released to the market in 1989 as a model for that year only. It was not made again in 1990 the same as your reel is with the AR on/off switch.
Here are the schematic links:
I am including the 1990 BBM VR for you to compare, but it is clear to see on this model they eliminated the AR on/off switch.
And what the heck, let's throw in the Bantam Black Magnums made in 1990 as well- also notice these do not have the AR on/off switch: (This is what I thought you had, except for the AR switch. Took a couple minutes to correct myself)
Something you should be aware of when servicing this old reel is that the flipping switch is very tricky to take apart and put back together. Most people who attempt to service these at home can get it apart, but can not get it back together with a working flipping switch. And your reel also has the tricky 2 speed lever mechanism.
Some of the parts for the flipping switch remain on the cover as it is taken apart and have to be reinstalled in the reverse order and it is tricky getting the spring released for disassembly, and back in place as it slides back together.
But just know these reels are built like tanks. If maintained they will last virtually forever. I still service a few of these at the shop and I sold one to a fishing buddy of mine who was just swearing up and down last week how much he loved using it for salt water. So here it is 30 years later and these reels are still being used today without replacement parts. That says something.
Your reel was the first of the Beast Master reels. Today some of them cost near $1,000.00.
Another issue with this old design is that the spool axle touches the inside of the pinion gear and these reels were prime candidates for shaft polishing and inside the pinion gear polishing. This is how "super tuning" was done back in the day. Today we no longer have to polish pinion gears to get extra casting distance and you rarely hear of anyone polishing drag washers too.
But, there is always timeless shimano where we can relive the past!
I use the Beast Masters and Black Magnum reels myself for many years... and there is one on ebay right now for sale- same as yours: