With respect to Chevy/GMC trucks, catalytic converter aplications are as follows:
1974 and earlier trucks - no converters were used on any vehicle (including passenger cars) prior to the 1975 model year.
1975 thru 1977 - all 50 states - catalytic converters were used with all engines (except for the 454 V8) on all standard 1/2 tons (i.e. all models under 6,000 lbs GVWR). Heavy duty 1/2 tons (i.e. Big 10's/Heavy Halfs), 3/4 tons, and 1 tons did not use converters.
1978 - 49 states except California - same rules as for 1975 thru 1977, except that catalytic converters were added to the 454 engine used in standard 1/2 tons (removing the previous exception noted above).
1978 California only - AND - 1979 all 50 states - ALL models up to 8,500 lbs GVWR use catalytic converters. Thus all 1/2 tons (including heavy duty models) and 3/4 tons use converters. Only 1 tons do not.
1980 thru 1986 - all 50 states - same emission laws as 1978 California and 1979 all states. However, Chevy/GMC added a line of heavy duty 3/4 tons with 8,600 lb GVW's which did not use catalytic converters. Light duty 3/4 tons (under 8,500 lbs gvwr retain the converter.
1987 to current - all 50 states - all fuel injected engines in all models use converters. Carburated models do not.
Therefore, your 79 3/4 ton did originally have a converter. (But your local area may not enforce the original rules, especially on such an old vehicle, so check before you spend the money on the repair). Hope this helps!