I've been a non-professional shadetree bike mechanic for over 40 years, and I have headset wrenches sized between 30mm, and 36mm. And sometimes wrenching on an old bike SAE wrenches are necessary.

On a 1980s Miyata with a Tange headset, you're going to need metric wrenches. You may be able to use a regular wrench for the locknut, but you're probably going to need a headset wrench for the nut/adjustable upper race.

I don't recommend using pliers or vicegrips on headsets and bottom brackets, because you will slip, and you will damage the chrome, and that leads to rust. Get the right tools for the job and use them.

You can try measuring to see what size wrenches you need, but you're probably better off taking the bike down to your LBS to match the headset to the wrenches you see (unless you are willing and able to buy an assortment of headset wrenches for your toolbox). While you're at it, get the bottom bracket wrenches your bike needs. Sometimes wrenches have a headset wrench on one end and a bottom bracket tool on the other end. Having your bike at the LBS when you are choosing wrenches sometimes makes the decision about what wrenches to buy for you. You might have a choice of headset wrenches that have bottom bracket tools on the other ends, some of which will fit your bike, and some which won't.