P.S.2 - Done on Earth. One cannot watch the skies!
If you insist on this, it cannot be done.
Your condition is equivalent to us living on a permanently clouded world. In that case, we would experience alternating light and dark periods and would have no way of hypothesizing what was happening. Understanding the universe would have to wait for the invention of aircraft that could pierce the cloud layer.
P.S. by watch, I assume you mean at any frequency.
If you relax this condition and allow naked-eye observations with no measuring equipment (so quite a bit less than the 16th century), then it's quite easy:
In mid-winter, at midnight, you look at the North Pole region of the sky (Big Dipper, Polaris, etc.) and make a sketch (or just commit it to memory). Then, six months later, you look again (mid-summer, midnight, somewhere South of the Artic Circle). Compare the stars with what you saw in winter. Everything is half-a-turn round the sky.
Go into a dark room, paint some fake stars on the wall and ceiling, light a candle in the middle of the room and play around with an apple or orange or other spherical fruit. You should soon get it.