Why would a 1989 GM truck brake warning light stay on blinking?

Check the antilock wire beneath the master cylinder.

Also the RWAL (rear wheel anti-lock) computer will store a (1 code at a time) code due to a faulty system. This code can be read by counting the flashes starting with the long flash as one and following with the short flashes there after (1(long)2(short)3(short)...and so on). The long flash always starts the new set of flashes. If the brake light stays on then a code reader will need to be used ($20 on ebay), which is read the same way.