Here you see two late (1954) 15/0 and 8/0 movements - a 670 and a 680, respectively - flanking a 713, the first of the 13/0 Lord Elgin movements. Note that the 713 is the same length as the 680, but only a bit wider than the 670, so they could be used in narrow cases as well as wide.
A number of Elgin's classic models were re-designed to hold the new 13/0 movements, like this Clubman...
The Clubman had been introduced around 1951 or so, and had been carried both 556 and 680 movements. This one's got a 713. Elgin also made a 13/0 version of the Black Knight.
Note that with the 713, Elgin went back to capping the 3rd and 4th wheel upper pivots, rather than capping the pallet. Also, all the 13/0 Lord Elgins made between 1956 and 1958 were Shockmaster movements, with Kif shock protection.
In late 1956, Elgin introduced a sweep second version, the 716. These were only made for a short time, and so they are relatively scarce. I've seen only 3 or 4 in two years of looking.
The most obvious difference between the 716 and the 713 is the presence of the sweep second bridge.
The sweep second hand is driven by an auxiliary wheel frictioned onto an extended upper 3rd wheel pivot. Because indirectly-driven sweep second hands tend to jump or skip, the sweep second drive wheel is actually composed of 4 parts - a hub, onto which fits a spring and two wheels The lower wheel fits loosely on the hub, but is linked to it by the spring. The other wheel fits friction-tight on the hub. When assembling, the lower wheel is turned 4-5 teeth against the pressure of the spring, then the sweep second pinion is inserted, holding both wheels with the lower on under tension. This keeps the pinion completely engaged at all times, and provides smooth sweep second motion.
However, if the spring breaks, or the wheel unit is put together wrong, or the lower wheel is not pre-tensioned, the sweep second hand will jump, stall, jerk, and otherwise not really sweep. One often finds the 3 movements equipped with this particular sweep second drive missing the wheel, or the pinion, likely because some previous owner couldn't get it to work right, and just had it removed.
In 1957, presumably to compete with Bulova's 23 jewel watches, Elgin made its own 23 jewel movements. The replacement for the 713 was the 718.
This watch, a Randall, was originally sold with the 713, then the 718, and I've seen them with later movements, too.
If you're thinking you don't see any difference between this and the 713, you're not wrong. Elgin added two jewels on the lower side. They capped the lower - but not the upper - pallet pivot, and they added one more jewel...
You can see the extra jewels in this picture. The setting with two jewels holds the cap jewels for the pallet and the escape wheel. The 23rd jewel you can see peaking at you from the center of the minute wheel, to the right of the cannon pinion. Elgin replaced the usual minute wheel post, machined into the plate, with a jewel pin. That comes pretty close to cosmetic!
The last of the pre-Durabalance Lord Elgin 13/0s is the 724. The 724 superceded the 716 much as the 718 superceded the 713. This watch was one of Elgin's Horizon Look series. I'll do another post on them...
This pre-restoration pic of the 724 movement shows the missing sweep second pinion.
In addition to the 713, 716, 718, and 724, Elgin also made two others. These were the Direct Read watches, also known as the Chevron and the Elvis watch. I don't own either of these, as I find them overpriced and not very attractive. But another collector has put together excellent pages on each of them - the Chevron, and the Elvis Watch.