IRAS 20319+3958 in Cygnus X South is a rare example of a free-floating globule (mass ~240M_{sun}_, length ~1.5pc) with an internal HII region created by the stellar feedback of embedded intermediate-mass stars, in particular, one Herbig Be star. In Schneider et al. (2012A&A...542L..18S) and Djupvik et al. (2017A&A...599A..37D, Cat. J/A+A/599/A37), we proposed that the emission of the far-infrared (FIR) lines of [CII] at 158um and [OI] at 145um in the globule head are mostly due to an internal photodissociation region (PDR). Here, we present a Herschel/HIFI [CII] 158um map of the whole globule and a large set of other FIR lines (mid-to high-J CO lines observed with Herschel/PACS and SPIRE, the [OI] 63um line and the ^12^CO 16->15 line observed with upGREAT on SOFIA), covering the globule head and partly a position in the tail. The [CII] map revealed that the whole globule is probably rotating. Highly collimated, high-velocity [CII] emission is detected close to the Herbig Be star. We performed a PDR analysis using the KOSMA-{tau}PDR code for one position in the head and one in the tail. The observed FIR lines in the head can be reproduced with a two-component model: an extended, non-clumpy outer PDR shell and a clumpy, dense, and thin inner PDR layer, representing the interface between the HII region cavity and the external PDR. The modelled internal UV field of ~2500Go is similar to what we obtained from the Herschel FIR fluxes, but lower than what we estimated from the census of the embedded stars. External illumination from the ~30pc distant Cyg OB2 cluster, producing an UV field of ~150-600Go as an upper limit, is responsible for most of the [CII] emission. For the tail, we modelled the emission with a non-clumpy component, exposed to a UV-field of around 140Go.