NTRS has Development of the fabrication and packaging techniques for the Echo II SATELLITE (I've finally started to learn from Organic Marble to check NTRS early), which is extremely detailed. Though I'm only skimming it, I believe section 3.6 "Gore Sealing" (starting on page 75 of the PDF / page 3-53) indicates that the gores were machine-sealed together using a sealing tape with an adhesive called "GT-301" at sealing temperatures of 300${}^\circ$F at a rate of 6 feet per minute. See particularly section 3.6.2.4 and Figs 3-29, 3-31. Section 3.9 indicates the "electrical continuity jumper strip" was installed with "a Gulton ultrasonic sealer, electronically and pneumatically operated"; Section 3.10 indicates the pole caps were also "attached to the sphere with GT-301 heat sealable adhesive." See Fig 3-37 for views of all the seals, despite its title.


The second picture is cropped from Fig 3-37.
Before finding that report, I was going to leave a slightly impoverished version of the following as a comment on the question but it seems at more constructive to leave these here instead:
Amusing Planet and SP-4308 indicate that the Echo I adhesive is owed to Gilmore Schjeldahl, and the Echo II report linked above says the GT 301 used for both lamination and gore sealing is also "a proprietary item of the G. T. Schjeldahl Co" (section 3.1.4).
BBBlimp and RCGroups appear to prefer adhesives to heat; so far, I've only found food bloggers sealing mylar with heat happily.
Good luck with your seals!