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Thank youThat should be a twist mount connector -- if your harness is in good shape but need just the 7-pin jack, I have on OE one from my '04. Hopkins makes a PnP replacement (#40920) that has the additional 4-pin socket. There are literally hundreds of OE connectors in junkyards. Otherwise you could use one of the online GM dealer sites to look up the OE number.
Rock Auto has replacement connectors, as well as the harness if needed: https://www.rockauto.com/en/catalog...7,electrical-connector,trailer+connector,2628
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