Generally, October is a very tough time to find a decent mule deer buck anywhere.
August to mid-September for bucks in velvet or late November through December in the rut are typically better times to find bucks across most mule deer “desert” country.
December-January is good down in the real desert on the New Mexico- Arizona/Mexico border. Still prefer the early season down there but you have to deal with a lot more snakes...
October is the toughest time of the year to find a good buck. The mature bucks tend to go nocturnal and brush up tight during the day at that time of year. Any additional pressure from vehicles or people tromping around and they will go invisible.
Bucks will be scattered and break off into singles or maybe doubles that time of year.
Good glass is key to finding them. A set of 15’s or even 10’s on a tripod and spend a lot of time standing/sitting behind the glass. Figure on spending 10+ hours a day glassing. Top end glass will allow you to stay at it much longer than the lower end stuff. A spotting scope to confirm and judge what you find in the binos.
Look for them in the roughest, most out of the way places that you can find. Look hard in any patches of taller brush, aspen pockets or along rimrocks.
Don’t skyline or bust into an area to glass like a bull in a china closet. Don’t be yakking! They can year you whisper over a miles away on a calm morning. Sneak in and use cover all the time. Figure on finding a bedded buck at least 1/2 mile away with only an antler tip showing in a sage bush. That good glass can help you find bucks 2 miles or more away. Be ready to have a buck blow up at your feet.
You might catch a mature buck up early in the morning but stay after it all day long. You should be looking for an antler tip sticking up In the brush from a bedded buck.
The locals have a lot more experience and time hunting those areas year after year. They also can run out morning and evening and scout or hunt through September so they have a HUGE head start on you coming in from out of state.
Although it can be hot, early September archery hunting is usually a lot better for seeing more bucks.
On my one and only rifle muley hunt in WY I experienced what you described for 8 days. Then I started glassing backwards and found a huge gnarly old nontypical bedded in a "bathtub" under a tree on an open hillside less than 1/4 mile from my camp. Truck after truck of glassing road hunters had passed by and couldn't see him lying there a couple hundred yards off the road.
Three truckloads of guys watched me belly crawl across the sagebrush to within about 70 yards of the buck, where I shot him in his bed. They never saw the deer.
I've killed some really big bucks with a bow, but I count this rifle buck among my most treasured hunting accomplishments.
Make every effort to sneak up on your glassing spots. Crawl the last bit if you need to.
There are tons of roads in that Wyoming sagebrush country and every ridge top has a two track running down it to the “best glassing spots”. Those bucks grew up seeing hunters drive out on those ridges and will bed right under the edges where they can’t be seen from above.
A big mature mule deer buck can live through a lot of hunting seasons by bedding on a ridge with a road on top and several miles to any roads in the bottom where they can be easily seen.
Have seen that over and over again up there.
Get out and walk with your pack and glass up to the ridges.
Lou, you see a deer?
I see a very nice pair there...
She looks pretty perky to me!