Good example Irishwolf.
Other spots to double lead back are anytime S3 has a viable path to 1 pt and he's playing with an expert in S1. For example, the score is 0-0, and the dealer who is a strong player turns down the
Our expert S1 calls next and leads the
S2 follows suit with the
And S3 has this hand:
S3 should play the AS on the first lead knowing a strong dealer can never have an unguarded Left in this spot. Then S3 should swing back with the Right on 2nd street, and then play his AD on 3rd street. The idea is, S1 is an expert, which means his Next range is gonna be very wide in this spot. That one trump lead may be all the trump S1 has. So when S3 sees a pathway to score a point he needs to take it. Yes sometimes this line will prevent his team from getting 2 points, but it's the best line to take given an expert S1's overall wide range.
Here's a way more obvious example:
The dealer turns down the
S1, an expert calls Next and lead the
S2 follows suit with the
S3 has
Notice when S1 leads the Left S3 can immediately deduce that's the only trump S1 can have. S3 holds the AS and the JS, if S1 had the 9s-Ks, he would lead the lower card. Therefore the Left is all S1 can have. Knowing this, S3 should play over the Left with his Right on the first lead, then lead the AS on 2nd street followed by his AH.
Same idea as above applies if an expert S1 calls next and leads the
and S3 has a hand like this:
Take the first trick with a bower, lead back the other bower, and play the AD. The exception being if S2-S4 show void in trump on the first lead then obviously S3 should not lead back trump on 2nd street. Not so obvious, if S2 and S4 plays the two other highest trump on first street, say S2 plays the KS and S4 plays the AS, S3 should gamble and hope S2-S4 are now out of trump. Yes it's logically possible for S2 or S4 to still have the

but I think the gamble is worth it. S3 should instead be thinking about playing for 2 now and lead the AD on 2nd street.