以下是不使用AnimatableData的方法：
我添加了第二个计时器，它每2秒通过偏移（0，-15，0，-15...）触发动画，永远重复。
如果isIdle变为false，我们只需要将offset设置为0，这个也会被动画化。我们重置所有的计时器。然后再次设置空闲计时器（3秒），当它启动时会启动动画计时器（2秒）。
（我还对GoLiveButton做了一些调整，使其自身包含所有相关状态，父视图只需控制isIdle）

struct GoLiveButton: View {
    
    @Binding var isIdle: Bool
    @State private var timer: Timer?
    @State private var animationTimer: Timer?
    @State private var animationOffset: CGFloat = 0
    
    var body: some View {
        ZStack {
            Button(action: {} ) {
                Text("Go Live")
                    .frame(width: 120, height: 40)
                    .background(Color.black)
                    .foregroundColor(.white)
                    .clipShape(Capsule())
                    .font(.system(size: 20))
                    .shadow(color: .black, radius: 4, x: 4, y: 4)
            }
            .offset(y: animationOffset)
            .animation(.timingCurve(0.38, 0.07, 0.12, 0.93, duration: 2), value: animationOffset)
        }
        .onAppear {
            self.timer = Timer.scheduledTimer(withTimeInterval: 3, repeats: false) { _ in
                self.isIdle = true
                animationTimer = Timer.scheduledTimer(withTimeInterval: 2, repeats: true) { _ in
                    animationOffset = (animationOffset == 15) ? 0 : 15
                }
            }
        }
        .onChange(of: isIdle) { newValue in
            if newValue == false {
                // reset all
                self.animationTimer?.invalidate()
                self.timer?.invalidate()
                animationOffset = 0
                
                self.timer = Timer.scheduledTimer(withTimeInterval: 3, repeats: false) { _ in
                    self.isIdle = true
                    animationTimer = Timer.scheduledTimer(withTimeInterval: 2, repeats: true) { _ in
                        animationOffset = (animationOffset == 15) ? 0 : 15
                    }
                }
            }
        }
    }
}

struct ContentView: View {
    
    @State private var isIdle = false
    
    var body: some View {
        
        ZStack {
            // for background tap only
            Color.gray.opacity(0.2)
                .onTapGesture {
                    print("tap")
                    self.isIdle = false
                }
            
            GoLiveButton(isIdle: $isIdle)
        }
    }
}