If the 'shadow' signal you refer to is BACKWARDS, then it IS from side two of the cassette... this can be attributed to three things that I can think of right off the top of my head:
a). a recording and/or playback head alignment problem. This can be corrected with a head alignment.
b). Misaligned tape guides which allow the tape to pass the playback head slightly skewed or misaligned.
c). Lastly, any thing affecting the head itself that would allow increased channel cross-talk... this can result from wear, bad quality control in the head manufacturing process, or just plain lousy head design to begin with! Obviously, the wear can be fixed (at least temporarily, eventually you'll have to scap the heads and replace them: assuming the machine is worth the investment). Bad design or bad QA is not something that you can resolve on your own.
Now, keep in mind that the above listed scenarios are only if the signal is backwards, indicating that it IS from the opposite side of the cassette.
If the signal is NOT backwards, (implying that the 'shadow' is on one or both of the FORWARD playing tracks), then its time to look at some other things.
First and most obvious question: Has this tape been recorded on before? If so, the problem can likely be attributed to the original signal NOT being fully erased when the new signal was recorded... this can be an alignment problem with the erase head (mechanical problem in nature) or an insufficient electronic signal sent to the record head which does not fully erase the existing signal before record (electronic problem in nature). Even some of the high power bulk erasers of yesteryear tended to leave a phantom signal on tapes. The only way to avoid this scenario is to only use new tapes when recording.
Another explanation may be PRINT THROUGH; it is a phenomenon that has long been known in the analog tape world... it occurs when the magnetic signal from a tape "bleeds through" to the portion of tape that is directly above or below it as it rests on a reel or spool. I suspect this is more prevalent when the recorded signal was causing near magnetic saturation of the tape to begin with. It occurs most frequently when the tape remains idle and unmoved for long periods of time. This is most certainly the case when the 'shadow' you hear sounds more like an ECHO... this is due to the signal being transferred in a forward direction and physically displaced only a short linear distance on the tape itself.
I tend to believe the PRINT THROUGH phenomenon was a much greater problem in the past when the tape oxides were near pure iron (FeO2) and mylar tapes were inferior to what they are now... I recall also (in the olden days) that the mylar was available in various thicknesses and tapes were sold according to reel size and length, the thinnest tape being almost 3x longer than the thick stuff! (If memory serves correctly, a 7 inch reel would typically contain 1200, 2400, or 3600 feet of 1/4 inch recording tape). Obviously, the 3600 footer(.5 Mil) tape was much more prone to PRINT THROUGH than the 1200 footer (1.5 Mil).
So ends my rambling and your history lesson for the day.
Good Luck in finding the source of your problem.
Cordially,
the guitar half of "RockNGunz"