Just a correction: the sequel was released in 1999 as Battlezone 2: Combat Commander. It was a AAA release and picked up the original alternate history storyline 30 years after the events of the first game, with all Earth-based factions now forming an official alliance and fighting a new common threat. It was insanely cool for a teenager back then.
While the sequel was technically far superior, I did miss the cold war tone of US vs Soviet conflict that was present in the first game.
I also loved the interpretation of Greek mythology through the "ancient aliens" lens (Hercules Brigade and all the other stuff, quite along the lines of what Stargate SG1 was doing at the time) that was revealed to you through briefings and pre-mission voiceovers. I think this was also more pronounced in the first game.
I still have a similar one. It's a vertical metal rod on a wooden base and a wooden ball on top. There's a ring that can slide along the rod. The ring has a tiny woodpecker figure mounted on a spring. With the ring in the top position you pull the bird and it starts pecking on the rod, moving the ring downwards with each peck, making that boinging & ticking noise. I used to love it as a kid. I still do. But I used to, too.
EDIT found a video of this exact one: https://www.youtube.com/watch?v=Szhxh1eEEL4