The Mind Thing by Fredric Brown, published in 1961.
The main (human) protagonist is Doc Staunton. Once he works out that the suicides are being caused by an alien he traps it by having his assistant Miss Talley tie him up:
Twice within the next hour she had to throw water in his face. Both times he’d been talking and had stopped in the middle of a sentence as his eyes went shut. It was six o’clock when it happened the second time; it would be dark within another hour or so. He doubted that he could possibly stay awake even that long, and certainly not much longer.
When he had dried his face with the towel, he stood up, swaying a bit. “Miss Talley,” he said, “it’s no use going on this way; even if I put carpet tacks on a chair and sit on them I’ll lose consciousness eventually. We’ve got to do one of two things. There’s danger in both of them, for you as well as for me, so I’m going to let you decide which we should do.
“One, I leave now while there’s time for me to walk to town—or at least to the nearest farm that has a telephone. I’ll take the shotgun and leave you the pistol. Maybe I’ll make it; maybe we’re overestimating the danger and overestimating the range at which the enemy can operate. Anyway, if I do make it I’ll see that you’re rescued. There’ll be state police, several carloads of them with shotguns and tommy guns… If I don’t get through—”
“No,” Miss Talley said firmly. “If you go, we both go, and I do the driving. Or afoot, if you think there’s any advantage to that. But why would there be?”
“It should keep me awake, for one thing. And for another, I can watch upward. As I said before, a heavy bird diving from a sufficient height would probably go right through the roof of a car as light as that, and kill whichever one of us it landed on. But your going with me wasn’t the alternative to my first suggestion. I don’t know whether the alternative is more dangerous, or less.
“It’s simply that I go to sleep, here in this room on the sofa, but that we take the precaution of having you tie me up first. There’s fifty feet of clothesline in the kitchen, so you can do a thorough job of it. First, our idea of what may happen to me if I sleep is only a deduction; we can be wrong. Second, if the enemy does take me over, I’ll be tied up so he’ll be helpless to make me do anything, such as injure you, and also unable to make me kill myself so he’ll be free to take another host. And that would mean it would be safe for you to drive into town and bring help.”