How do I account for an insurance loss on a rental property in 2013, which was restored with insurance funds, as part of basis when property sold in 2018?

Let's say for example you had a rental that cost $100K and it had $35K of damage.

You fixed it and it cost you $35K and the insurance company paid you $35K.

The insurance $35K is not income it only reimburses what you fixed back to the way it was.  The tax impact is $0 in this case, and the cost is still $100K (what you paid for it).

Now say you only got $34K in the example above, then the $1K might be deducted as an expense in 2013 or added to the basis or cost of the rental, if so then the cost would be $101K.

So,  the cost of restoration over what the insurance paid, if any, can be added to the cost basis for the sale in 2018, thereby reducing the taxable gain.   Is this correct?

It should have been done in 2013, either added to the cost or expended (depending on amount).

And yes, if it was added to the cost it would reduce the gain on the sale now.