Steering shake and accelerating in a straight line in a rwd vehicle are almost mutually exclusive.
Although you seem to know what death wobble is or learned the word. Nothing in the back half of the drivetrain gonna make death wobble.
That said, no one knows your weight or weight distribution. You could have enough weight in the back and bad enough steering components that just a little weight transfer off the front makes it squirrelly.
And for those saying tires, good guess since they’re likely old AF but square tires aren’t only symptomatic under accelerating.