If, as a prescriptivist, you disregard the elision of the words I was as the source of the technical error, then the apparent error reduces to the conjunction of two independent clauses with an ambiguous subordinate clause.
The subordinate clause is (in simplified form) while driving. The first independent clause has no subject other than recollections, which cannot be directly reconciled with the pronoun subject I of the second independent clause, so it is ambiguous as to who or what is driving (Recollections may drift, but as Cascabel commented, they do not drive.)
I'll illustrate by simplifying the sentence first without the subordinate clause:
Recollections drifted into the mist, and I thought of the Indians.
On the other hand, with the subordinate clause, it becomes something like this, where the ambiguity can be seen:
While driving, recollections drifted into the mist, and I thought of the Indians.
Including the elided words we have a subordinate clause that may refer to one or both independent clauses, but it does eliminate the ambiguity entirely:
While I was driving, recollections drifted into the mist, and I thought of the Indians.
It's not uncommon to omit the subject of a subordinate clause when it can be inferred from the independent clause. In this case, having two independent clauses with irreconcilable subjects might offend someone driven by prescriptive grammar. But literary license overrules this, especially in popular works, where sins are easily overlooked.