It’s called craquelure. (Forgive my short explanation. I have to get up in 4 hours.) In addition to applying thick layers of paint Rembrandt used varnish. All of this dries at different times, which leads to the cracking effect. It’s more a condition of how it was painted and the media the artists used and less about trying to achieve the effect outright.
Source: I have a phd in art history, and publish and teach in this field
Fun fact: the Night Watch is an inaccurate title. The title is actually Militia Company of District II under the Command of Captain Frans Banninck Cocq or The Shooting Company of Frans Banning Cocq and Willem van Ruytenburch. It’s known as the Night Watch because of dirt and varnish—the varnish yellows over time. This changed after extensive restoration. Also, the painting has been vandalized several times. In one unfortunate event in the ‘70s a person took a knife to it.
For more on craquelure see: https://en.m.wikipedia.org/wiki/Craquelure.
(Edited to clarify that varnish yellows over time)