I would attribute it to the increase in tax rate paid for FICA taxes. In 1988 the Feds were collecting 2.8% of GDP more than they were in 1980 from the increase in FICA rates. From 1981 - 1987 over half of the increase in revenues came from increase in FICA revenues.You said it "didn't work" when Reagan or Bush did it, but revenues did increase during those years. I wouldn't necessarily attribute that to the tax cut as much as the fact that revenues almost always increase.
Tax cuts don't increase revenues nearly as much as tax increases do.