Here's my thoughts on the subject.
As SRW cites, the runner must touch bases in proper reverse order. And the "last time by" policy isn't accepted. So, having missed 2nd, the runner must return and touch 2nd.
Assuming he does return to touch 2nd, in order to return to 1st in proper reverse order, he must return again and retouch 1st. In effect, since he missed 2nd, the initial touch of 1st is invalid because it happened out of order.
It may be semantics, but the OP doesn't specify live ball or dead ball appeal. If a live ball appeal by tagging the runner (who is in jeopardy), I would accept the appeal as being "clear enough" in its intent. If a dead ball appeal, I believe the defense would have the opportunity during that dead ball period to reasonably explore any realisticly available appeal (in other words, I would answer the initial appeal in such a way as to suggest they might be asking the wrong question, without telling them what question to ask).
Or, I could be wrong
.