您可以：

library(tidyverse)
df %>%
  pivot_longer(cols = -id,
               names_pattern = '(.*)_(.*)',
               names_to = c('timing', '.value'))

其中：

# A tibble: 6 x 4
     id timing value date 
  <dbl> <chr>  <chr> <chr>
1     1 first  A     2001 
2     1 second A     2003 
3     2 first  B     2010 
4     2 second NA    2014 
5     3 first  NA    2003 
6     3 second D     2007

注意：只有当你把second_values列重命名为second_value时，这才有效。我想"values"只是一个打字错误吧？
根据@Maël的建议，选择更简单一点：

df %>%
  pivot_longer(cols = -id,
               names_sep = '_',
               names_to = c('timing', '.value'))

可以尝试这样的事情吗？

library(tidyverse)

df <- data.frame(id = c(1,2,3),
              first_value=c("A","B","NA"),
              second_values=c("A","NA","D"), 
              first_date=c("2001",2010,2003),
              second_date=c("2003",2014,"2007"))

bind_rows(
  df %>% 
    select(id, first_value, date = first_date) %>% 
    pivot_longer(cols = "first_value", names_to = "timing"), 
  df %>% 
    select(id, second_values, date = second_date) %>% 
    pivot_longer(cols = "second_values", names_to = "timing")
  ) %>% 
  relocate(id, timing, value, date) %>% 
  arrange(id)

最后两行只是为了获得与您发布的格式/顺序相同的格式/顺序，所以可能会被省略。