Never seen a kit without accelerator pump cup. Can't "rebuild" any older carb without that.
ALL the usual online guys I buy from show an accel pump stem w/cup in their 28/228 kits. Better recheck you supplier's website and picture of parts as BillB says. Source: Mike's, Carb Doctor, Ebay, Misc.
Tell us where you got kit so we will know what's up.
The three materials used for accelerator pumps are leather, Buna-N rubber, and Viton rubber. If not Viton or equiv, E10 with eat them up. Good is usually Blue.
Leather is usually red and Buna-N is usually Black. Old kits from Ebay advertised as NOS are no good. Anything with rubber seals, O-rings, shock absorbers, carb kits, etc. that are "NOS" are NO GOOD anymore. They are outgassed, dried up, thermal cycled 1000 times, degraded and made from old compounds. Unless they were hermetically sealed and kept in a #2 mayonnaise jar on Funk and Wagnall's front porch. It's all in the logistics.(sorry pking)
