combining 2 columns using ifelse dropping a variable R - r

Question

I am trying to combine the male and female columns I have created into one column. I tried using some answers I found on stack, but the second sex I queried was excluded.
Build Data Frame:
ID <- 1:10
SPAYDT <- c("", "2011-12-01", "", "2006-05-01", "", "", "", "", "", "")
SPAYDTU <- c(1, NA, NA, NA, NA, NA, NA, NA, NA, NA)
NEUTDT <- c("", "", "", "", "", "", "2013-03-01", "", "", "")
NEUTDTU <- c(NA, NA, NA, NA, NA, NA, NA, 1, NA, NA)
df <- as.data.frame(cbind(ID, SPAYDT, SPAYDTU, NEUTDT, NEUTDTU))
df
The goal is to have a column for sex, formated as a factor with 2 levels - Male and Female
It should say female if the SPAYDT or SPAYDTU have a value in them, and male if the NEUTDT or NEUTDTU have a value in them.
What I have tried:
using a nested if-else statement to build one sex column
making two columns then combining using
df$male <- ifelse(NEUTDT!="", "Male",
ifelse(NEUTDTU=1, "Male", NA))
df$female <- ifelse(SPAYDT!="", "Female",
ifelse(SPAYDTU==1, "Female", NA))
df$sex <- ifelse(!is.na(df$female), df$female, df$male)
and
df$sex <- ifelse(SPAYDT!="", "Female",
ifelse(SPAYDTU==1, "Female",
ifelse(NEUTDT!="", "Male",
ifelse(NEUTDTU=1, "Male", NA))))
However, no matter what I do, the sex column at the end only has one sex. I made sure my df was attached for use of column names as variables. I tried restarting R and running the setup code again. I just don't know why the ifelse statement is ignoring the second sex input.
Any help is greatly appreciated!
Clarifications:
In the larger dataframe I am working with I have done data clean up so that each ID only corresponds to 1 sex. Sorry about the mistake in the code.
Desired output:
ID <- 1:10
SPAYDT <- c("", "2011-12-01", "", "2006-05-01", "", "", "", "", "", "")
SPAYDTU <- c(1, NA, NA, NA, NA, NA, NA, NA, NA, NA)
NEUTDT <- c("", "", "", "", "", "", "2013-03-01", "", "", "")
NEUTDTU <- c(NA, NA, NA, NA, NA, NA, NA, 1, NA, NA)
SEX <- c("Female", "Female", NA, "Female", NA, NA, "Male", "Male", NA, NA)
df <- as.data.frame(cbind(ID, SPAYDT, SPAYDTU, NEUTDT, NEUTDTU, SEX))
df

Answer 1

Is this what you are after?
ID <- 1:10
SPAYDT <- c("", "2011-12-01", "", "2006-05-01", "", "", "", "", "", "")
SPAYDTU <- c(1,NA,NA,NA,NA,NA,NA,NA,NA,NA)
NEUTDT <- c("", "", "", "", "", "", "2013-03-01", "", "", "")
NEUTDTU <- c(NA,NA,NA,1,NA,NA,NA,NA,NA,NA)
df <- data.frame(ID, SPAYDT, SPAYDTU, NEUTDT, NEUTDTU)
df %>%
mutate(
sex = case_when(
NEUTDT!="" | NEUTDTU==1 ~ "Male",
SPAYDT!="" | SPAYDTU==1 ~ "Female",
TRUE ~ NA_character_))