Suppose the first mortgage holder forecloses, the property is sold at auction, and the mortgagor redeems the property within the redemption period.   Would such a redemption reinstate the 2nd and at the same time move it into first position ? 

No, the foreclosure wipes out the second mortgage, the redemption is for the lien that foreclosed and all SUPERIOR liens.  Since the 2nd is inferior, it is wiped out.  To protect the 2nd's interest, the second would have to foreclose first, and possibly pay of the first, or just pay off the first.

Oh OK.  Thanks !

@Robert Carpenter
Let me know if you need any help I specialize in foreclosure in northern jersey

In California, and I suspect New Jersey, using the term "wipes out" is misleading. More appropriately, it should really be "wipes off." A junior-lien-holder's interest in the property is lost, but the junior lienholder can still sue you personally on the promissory note, thus not wiped out.