Tinker Tom is a wild eyed maniac who wants to inject me with strange chemicals. Should I let him?
Solution 1:
When you first go into railroad HQ, somebody says to keep him happy cause he's got all the cool stuff.
If you let him give you the shot, he will offer you items that he creates for you because he then 'trusts' you.
Solution 2:
Tinker Tom's shot only seems to drain your health (well, it does have battery acid in it) and has no real effect or grants any perks as far as I can see. I guess he really is at least partially crazy...
Solution 3:
All I know is that the serum drains your health to one punch death and lets Tinker Tom sell you stuff. Deacon likes it, while Danse dislikes it