If you have a reasonably clear photo from the seller you can measure directly. This only works because there are known-size elements in the same plane as the cage that you want to measure.
What I would do is measure the derailleur you have, and count the teeth on the idler gear you'll be using as a reference just to make sure they're the same on both your one and the on you're considering.
This is a random image I chose because it has the cage flat to the plane of the picture so it's easy to discuss. If you can get the seller to take a similar photo it'll make your life easier (eg by pressing the cage flat on a table, then taking a photo looking straight down at it).
The red lines show the size of the idler. Measure in pixels if you have an image program that shows you the length of the line you're drawing in pixels, or use a ruler on your screen if that's all you have. The yellow line is one possible option for measuring the cage length, but it's not ideal because it's going from the back side of the cage to the front, so if there's any tilt to the cage your measurement will be off. Or you could measure from the text on the cage to the edge of the bolt. But for best accuracy make the line as long as possible - measuring the text size is likely to give a huge uncertainty because there are so few pixels available (read up on quantisation noise in wikipedia or this introduction if you're interested). So I'd try to use the green line instead.
You need to get four measurements.
- size of the idler you have (in millimetres or units of your choice)
- size of the idler you might buy (in pixels)
- length of the cage of your derailleur (millimetres or whatever)
- length of the cage of the one you might buy (in pixels)
From that you can calculate the pixels per millimetre of the idler gears, then divide by the pixel length of the cage in the picture to get the millimetre length of the pictured derailleur. Compare that to the one you have and decide if it's the right size.
If you are really concerned you could do this for the reference pictures on the Shimano website to get an idea of the lengths that are available. That way you can guess which actual derailleur is for sale, rather than possibly rounding incorrectly (eg if you calculate 100mm from the picture and the actual options are 95mm, 102mm and 115mm you can either guess it's the 102mm one or compare the pcitures more closely to get a feel for the correct choice. Without the reference pictures you're left with "my one is 103mm, the seller pictures gives 100mm... that's close enough)
This all substitutes effort on your part for effort from the seller, but it also means you know more about how accurate the measurement is. I find it's often easier to measure the picture than the derailleur - note that the green line crosses through the pivot in a way that a tape measure can't do. To fake that lay the tape or ruler parallel to what you want to measure and as close to it as possible while keeping it in the same plane, then take the photo. (it's probably easier to buy a cheap vernier caliper and learn how to use it)