>>(No vaccine exists for HSV-1.)

There were a couple of matches in clinicaltrials.gov, notably HerpeVac Trial for Young Women (Trial record 3 of 3 for: HSV-1 vaccine).

Results published in Efficacy results of a trial of a herpes simplex vaccine

…vaccine efficacy was 20% (95% confidence interval [CI], -29 to 50) against genital herpes disease. However, efficacy against HSV-1 genital disease was 58% (95% CI, 12 to 80). Vaccine efficacy against HSV-1 infection (with or without disease) was 35% (95% CI, 13 to 52), but efficacy against HSV-2 infection was not observed (-8%; 95% CI, -59 to 26).

So not particularly efficacious. But maybe switch to (No efficacious vaccine for HSV-1 is available) (?)