Wouldn't it be cheaper/easier to just buy one of these and wire it into the connector?
https://www.amazon.com/BESTEK-300W-Power-Inverter-Adapter/dp/B07Y9M1H88?ref_=s9_apbd_omg_hd_bw_b2RkW&pf_rd_r=92K5TKT119G0JCSES4CF&pf_rd_p=ef88a328-5802-52f1-a22b-1f46a5201df0&pf_rd_s=merchandised-search-10&pf_rd_t=BROWSE&pf_rd_i=583328