HP LaserJet 1320: Alternating periods of "proper duplexing" and "failure to flip the sheet"

[wrarus]

My 1320 has been a trusted companion for a long time now but recently has been acting up. A typical scenario is as follows:

If I have a job which requires multiple two-sided sheets as output, the first several sheets, up to 4 or so, come out properly printed on two-sides. However, after those sheets the printer fails to flip side 2, forcefully ejects it (often landing on the floor), and then prints side 1 on a separate sheet.  If I immediately print again that failure-to-flip behavior continues; but if I give the printer a several minute rest it often reverts to giving a few properly printed sheets before going rogue again.  

Suggestions for a remedy are welcomed. Thanks.

[Valsimot]

It smells like Tray 2 sticky solenoid.

Check the video at 1:53 what happens with a sticky solenoid.

If you remove a right cover, you will found a Tray 2 solenoid that gets sticky, when you remove it you will figure what I mean.