Jamaican Field Cricket Gryllus assimilis

Jamaican Field Cricket Both adults have "cerci" and are fully-winged.
Jamaican Field Cricket Female also has ovipositor.
Jamaican Field Cricket Nymphs have several moults, "cerci" but no wings.
The Jamaican Field Cricket, also called the Jamaican Brown or Silent Cricket (not silent but quieter than House Cricket), is native not only to Jamaica but also to much of the Caribbean, southeastern US, Central and some of South America. Other related American field crickets that used to be considered the same species have been split to separate species in recent years.
Jamaican Field Cricket
Jamaican Field Cricket
Jamaican Field Cricket nymphs
The Jamaican Field Cricket is commonly bred as food for captive insectivores since the previous species used, the House Cricket (a different genus), became susceptible to a paralysing virus to which the Jamaican is immune. They are similar-looking, similar-sized brown crickets (the Jamaican also has a black phase).
Jamaican Field Crickets
Jamaican Field Crickets
Jamaican Field Cricket
One key distinguishing feature seems to be the shiny head which has light stripes longways in the Jamaican and has a single band widthways like a headphone in the House Cricket. (The Banded Cricket which is also brown, has two body bands as well as the head band.) Some crickets sold in the pet trade as Jamaican, are the similar-looking South American G. locorojo which has 3-4 pale longitudinal stripes on its reddish brown or dark brown/black head.
The Jamaican also has a matt pronotum rather than shiny since it is covered in tiny hairs.