Would I have to know anything to carry stakes & a hammer & be fit enough to walk around all day?
Wind River, knowing the attitude of most here when it comes to do DIY surveying, I'm surprised you haven't been torched yet.
You are, by the way dabbling on the fridge of illegal activity.
In most places, surveying your own land is legal. If you, on your own, were to try to set a corner between your land and a neighbor that is clearly illegal anywhere in the US.
Even doing what is legal, however, presents a big risk you will misinterpret something if you don't have the proper background, and create problems for yourself down the road. Your questions started out with a little education, and then got into waters that we don't think you are ready to tread.
Keep on learning, but if the surveyor who made the plat can show you the corners, that is by far the most prudent route.
On most subdivisions there are bearings on each line. So we would set up on one corner, backsight another corner and turn the appropriate angles to other corners. If there are no lot corners, you can use the control in the street and work from there. And you are correct that we always zeroed the instrument on the backsight so we could turn the calculated angle. Some of the “smarter” surveyors would calculate everything to azimuths and then sight the azimuth on the backsight and foresight to the azimuth they wanted to stake out. Most of us kept it as simple as possible for everyone and only turned angles to the right.
When surveying in rural areas we would use the GLO bearing for a line between a section corner and a quarter corner as our Basis of Bearings. If you could not see between them we ran a traverse from one to the other, inversed the bearing from the coordinates and rotated the traverse to the GLO bearing.
Now if you wanted to set up your TS20 out in the middle of nowhere and get a starting bearing, you could just set up the instrument, zero it, step back about six feet, line your hand compass up with the scope and read the bearing on the compass. Then if you want to orient it to North, just turn the appropriate angle to get North to orient the scope looking North and there you are. You should not really worry about the accuracy more than that because you are only using a hand compass and probably also have lost additional accuracy due to declination. You could even set a stake, stand over it and have another person drive a stake where you tell them to mark North, set up your gun and you are ready to go. I would guess that most people would only be accurate to about ±5° if the declination was within a degree or two. (That would be what you described, and it would work).
I wrote this up last night, so things may have progressed beyond this. It sounds like you have identified two of your property corners on the same line and are working from that. If that is the case, you would probably be OK. You definitely have to be sure of the corners. Duct tape has nothing to do with finding a corner unless the surveyor ran out of flagging!!!