Maybe this article could help you Dr Mahmoodzadeh https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4300707/...

Their recommendation is based on a combined treatment based on Surgery + Thyrokinase Inhibitors and adjunctive therapy

Regarding the management of esophageal GIST three pillars need to be considered and linked together: i) appropriate pre-therapeutic histological diagnostics including biopsies, ii) alternative surgical procedures (i.e. radical resection vs. local tumor excision/enucleation), and iii) administration of tyrosine kinase inhibitors (e.g. imatinib) in different settings (i.e. neo-adjuvant, adjuvant, additive). Since controlled trials for esophageal GIST are missing due to the low incidence, neither the best surgical procedure, nor the impact of adjuvant or neo-adjuvant tyrosine kinase inhibitor therapy is well established. Currently, complete surgical elimination of the tumor appears to be the only curative therapeutic option in the management of non-metastatic, resectable esophageal GIST

Also, in my own experience (gastric GIST), we decided to performed a  local tumor enucleation and a therapy with tyrosine kinase inhibitors (imatinib) for a year. After the first 6 months we decided to duplicate the imatinib doses. In addition to monitoring with PET CT. 

On first 6 months the patient wanted to dismiss the imatinib for the side effects, so was necessary to explain such adverse effects

The main types of treatment used for GISTs include:

Surgery

Targeted therapy drugs

If you know it is a GIST prior to surgery then depending on its size, presentation and patient fitness options are surgery or bro-adjuvant TKI. Always tempting to downsize prior to any surgery particularly if a local resection is being considered (rather than formal oesophagectomy).

Generally it is much more common to get leiomyoma’s in the Oesophagus.

After surgery if a GIST is proven than adjuvant TKI is recommended for high risk GISTs in the Uk. Their role in medium risk lesions is controversial.