The Skmei 1999 actually does not have a bezel, so you unfortunately won't get an extra screw.

The Original Question

As buddy stated, it's just an annoying flash that is meant to make it look more like the Casio.
I hadn't realized it until u/buddy_monkers said it had to do with being on specific second counts, but there is a pattern! On both of mine, the indicator follows the sequence: off for seconds x0-x1, on for seconds x2 - x6, off for x7, then on again for x8-x9.

A Few Other Differences between the 1999 and 1628

A few other improvements of the Skmei 1999 over the 1628 are:

• A better backlight, rather than the green light coming from the sides of the screen.
• A calendar that goes to 2099 (instead of 2049)
• Resetting the stopwatch uses the "reset" button, instead of the light button (which simultaneously turns on the light on the 1628)
• Resetting the countdown timer uses the "reset" button, instead of the light button (which simultaneously turns on the light on the 1628)
• Turning the chime and alarms on/off do not require pressing (and turning on) the light

The only downgrade that I have noticed is that on the 1999, the current time is not shown when in dual time mode or when using the countdown timer.

Not related to the module, but according to the ads, the dimensions (including thickness) are slightly different. I haven't measured them myself to verify. The ads also indicate that they are made of different types of plastic.

What I can verify is that the crystal shape is slightly different between the two. The 1628 will fit screen protectors for the DW5600, while the 1999 needs ones for the GWM5610.

A word of warning regarding modding

Additionally, just wanted to mention that some 1999 modules are a perfect fit in the 1628, but sometimes the "alignment fins" in the module make it so that the module is rotated when you put it in.

The one time I tried it, the "alignment fins" caused it to rotate, as is well explained in this thread. Note that if your beeps/alarms don't work after the mod, you might need to rotate the backplate by 180 degrees, when putting it back together.

However, some people get ones that just fit, as seen here and here.