The way I work it out (very roughly) is that Eligius generally solves 20+ blocks per day, so 13 will likely take around half a day.
The other way of looking at it is to follow the link to the payment queue, find your address therein, check the "Age" column.
Say, for example, your Age is 1 day 22 hours.
Then look at the top of the queue and at the bottom of the first block. Don't look at the actual top of the first block as that may worry you.
There should be a lot of entries there with a similar age (say for example 2 days 10 hours).
Subtract your Age from that Age and the difference (12 hours) is (roughly) how long it will take you to work your way to the top of the queue.
The actual real amount of time is how long the pool actually takes to solve those 13 blocks that will get you to the top, plus the variance of any more people joining the queue ahead of you as their thresholds are passed and they turn out to have been waiting longer than you for a payout.

Hope that helps, but now I write it down it does sound a little tricky and it took me a while to figure it out myself. YMMV.