I am fixing a house that was build in the 1950s. Completey redoing the wiring and I have basment pull string lights mounted to the juntion boxes that feed the upstairs bedrooms (one junction box per room). Each bedroom has its own 15amp circuit wired with 14/2 NM. My question is two part. 1) can a light in the unfinished basment be connected to the outlet circuit that powers the bedroom above. 2) if it is allowed does the light need to be on a pigtail mounted to its own box. This house is in south west Michigan

1. Yes
2. Why not switch loop the pull chain to a wall switch and leave it where it is?
3. If you are redoing all the wiring, I believe you need to upgrade to GFCI's and AFCI's where required.

If you are completely redoing the wiring you must meet today's code which likely calls for arc faults in the bedrooms and GFCI in unfinished basements, can't mix them. Best to call the local building department and see which code they follow and what they will accept.