Transmission shifts only with added help

Hi. I'm new on the forum; just got a '75 KZ400 running. I have a strange tranny problem; the clutch works fine and has nothing to do with it.

I can start the bike in neutral and select first gear, which works fine. I can then upshift to second. That's good, too. But when I try to go into third, nothing happens; it won't shift.

So I noticed that the shift lever doesn't seem to return to its normal position. It just stays "up" when I go up into second. If I gently tap it back down when I'm in second, and then upshift to third, it works. It seems the shifter just stays where my toe puts it, with no "return" action, so it can't be ready to grab the next gear.

My test track isn't long enough to try additional gears, but I'm suspecting that there's a return spring somewhere that's weak, or something on the shift drums is gummed up.

I've put only about 5 minutes on the bike since I got it running. (It sat for maybe 5 years before I got it.) Yes, I have changed oil and filter.

Should I just put more time on it and see if it frees up? Is this a common thing? What should I look for? Is there an easy fix? (I have just downloaded the manual, but you all seem to have a lot more practical experience.) Thank you.