I replaced headlight on 2002 trailblazier now daytime running

There is a microprocessor in the instrument cluster that grounds the DRL relay - do you know if the relay has power from the headlight fuses and is being grounded by the processor ?

Your van has dual diligent headlamp bulbs, that means each headlight has one bulb that serves as high beam and low beam. What has most likely happened is on one side the low beam filament has burnt out, and on the other side the high beam filiment has burnt out. The daytime running lights are just the high beam filament running on reduced power, so if the high beam doesn't work on one side, that same side will have no daytime running light. Replace both headlamp bulbs with matching, good quality bulbs.

Open the hood, then remove the headlight. To remove the headlight, there are 2 "L" shaped brackets, one on the left, one on the right. Rotate them both toward the front of the car, then pick them straight up and the headlight will come out. Now, you have to fiddle with the daytime running light socket a bit. You have to twist it to the right and it will pop out. However, to twist it, there is a plastic piece on it you have to depress to get it out of the way of a 'stop' that protrudes from the daytime running light housing. Take out the old bulb, put in the new one, slide the bulb back in at the angle you took it out, then twist it back and it will snap in place. (The snap is the sound of that plastic piece hitting the gray 'stop'.) Put the headlight back in and you're done.

The blinking light is telling you that you have a headlight out, if you look the service light should be coming on when the light stops blinking.
Replace the head light and all should be fine.

Sounds like you need a bulb,the daytime running lights send power to the high beam wire so they look like low beam lights are on but really they are high beam lights running on low voltage.

You can tell by looking at the headlight switch. Without daytime running lights, the switch only has 3 positions, "Off","park" and "headlights" with daytime there is a fourth position to use or not to use the daytime lights.

Check for broken cables, proper ground to body, if headlights have diferent circuits if does, check individual fuses.

Just replace the bulbs,they don't last that long.The trick is remove the headlights,there is (2) pins on top of headlights.
Remove the pins and pull the headlights out the way.The light sockets are right below!

although the underhood relay panel is common, I'd check your headlamp bulbs first, these are cheaper than the fuse box. The daytime running lights work off the high beam circuit, thus, a blown highbeam bulb could be the culprit, the fusebox solution was more common on 2001 and up modles, although it's a definite possibility.

Check the connector to the DRL module behind the headlight switch, it may have burnt contacts.