MART-1 Antigen With or Without TLR4 Agonist GLA-SE in Treating Patients With Stage II-IV Melanoma That Has Been Removed by Surgery

Inclusion Criteria:

* Central pathology review submission; Note: this review for MART-1 positivity is mandatory prior to randomization to confirm eligibility
* Human leukocyte antigen (HLA)-A2-positive
* Histologic proof of stage II, III or IV melanoma that has been completely resected or completely treated with ablative therapy (ex: stereotactic body radiosurgery, radiofrequency ablation, cryoablation) with no current evidence of disease, as demonstrated by imaging within 2 months (stage III or stage IV; must be computed tomography \[CT\], magnetic resonance imaging \[MRI\], or positron emission tomography \[PET\]/CT) or 6 months (stage II; may be chest x-ray, CT, MRI, or PET/CT)
* Absolute neutrophil count (ANC) \>= 1500 mL
* Hemoglobin (Hgb) \> 10 g/dL
* Platelets (PLT) \>= 50,000 mL
* Aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN)
* Alkaline phosphatase =\< 3 x ULN
* Ability to provide informed consent
* Willingness to return to Mayo Clinic Rochester for follow-up
* Life expectancy \>= 12 weeks
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2
* For women of childbearing potential, a negative serum pregnancy test =\< 7 days prior to registration
* Willingness to provide mandatory blood samples for correlative research

Exclusion Criteria:

* Uncontrolled or current infection
* Known standard therapy for the patient's disease that is potentially curative or proven capable of extending life expectancy
* Known allergy to any of the vaccine or adjuvant components, including eggs
* Any of the following prior therapies with interval since most recent treatment:

  * Chemotherapy =\< 4 weeks prior to registration
  * Biologic or immunologic therapy =\< 4 weeks prior to registration
  * Radiation therapy =\< 4 weeks prior to registration
* Failure to fully recover from side effects of prior therapy or surgery
* Any of the following:

  * Pregnant women
  * Nursing women
  * Women of childbearing potential or their sexual partners who are unwilling to employ adequate contraception (condoms, diaphragm, birth control pills, injections, intrauterine device \[IUD\], surgical sterilization, subcutaneous implants, or abstinence, etc.)
* Known immune deficiency, including human immunodeficiency virus (HIV) infection
* History of systemic autoimmune disease, as patients with ongoing autoimmunity may be at an increased risk of autoimmune toxicity from the study vaccine
* Current or recent (=\< 4 weeks) use of immunosuppressive medications including systemic (inhaled, oral, or intravenous \[IV\]) corticosteroids; Note: use of corticosteroids in doses not exceeding those used for adrenal replacement is acceptable
* History of brain metastases; EXCEPTION: patients with a solitary brain metastasis that has been completely resected, and who have no ongoing central nervous system (CNS) symptoms and an MRI documenting no evidence of CNS disease at least 3 months after resection and within 30 days of registration, are eligible for treatment
* Other active malignancy =\< 5 years prior to registration; EXCEPTIONS: non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: if there is a history of prior malignancy \> 5 years prior to registration, the patient must not be receiving other cancer treatment