If built in 1998 there should be more wires the box than just black wires.
The power connects to the HOT wire on the timer
The wire going to the lights connects to the LOAD wire
The white wire on the timer connects to a group of 2 or more whites that will be in the rear of the box
Then ground to the ground wire if on the timer
If you do not have any white wires in the rear of the box, the home must be wired in conduit, since all other wiring in 1998 has a white wire in every cable.
The old timer was only a 2 lead timer and did not need a neutral.
The new one needs the neutral to provide its own power source with the HOT wire.
If you do not have whites available in the rear of the box for connecting to the white, then you can either add a wire in the conduit or will have to get a 2 wire timer.
Intermatic makes the 2 wire timer still today. Most manufacturers have adapted to the neutral need wire unfortunately.
I can recommend the proper timer if you need the 2 wire type, just let me know.
Something is strange on your timer, as I have found the original one. The HET01 is shown that it also has the same 4 wires on the timer. Red,black,white and green.
Not sure how yours only has 2 black wires?
CLICK HERE to see the HET01 Does yours not match?