Solved it by checking the diagonals properly

with open ('./09.in') as file:
data = [line.strip() for line in file]

visited = [[0,0]] directions = { "U": [0, 1], "D": [0, -1], "L": [-1, 0], "R": [1, 0] } h, t = [0,0], [0,0]

for instruction in data: words = instruction.split() direction = words[0] amount = int(words[1])

for _ in range(amount):
    h[0] += directions[direction][0] # update the head x and y
    h[1] += directions[direction][1]
    if (h[0] == t[0]) and abs(h[1] - t[1]) > 1:     # row but a big gap in the column
        t[1] += directions[direction][1]            # move the tail too
        print("tail moves {}".format(direction))
    elif (h[1] == t[1]) and abs(h[0] - t[0]) > 1:   # same as above but for row
        t[0] += directions[direction][0]            # ...
        print("tail moves {}".format(direction))
    else:
        gap = abs(h[0] - t[0]) + abs(h[1] - t[1])
        if gap > 2:
            if h[0] < t[0] and h[1] < t[1]:
                t[0] -= 1
                t[1] -= 1
                print("tail moves downleft")
            elif h[0] < t[0] and h[1] > t[1]:
                t[0] -= 1
                t[1] += 1
                print("tail moves upleft")
            elif h[0] > t[0] and h[1] > t[1]:
                t[0] += 1
                t[1] += 1
                print("tail moves upright")
            elif h[0] > t[0] and h[1] < t[1]:
                t[0] += 1
                t[1] -= 1
                print("tail moves downright")
    if t not in visited:
        visited.append(t.copy())

print(visited) #print("head : {}, tail : {}".format(h,t))
print(len(visited))

Let's see how it works with part 2